What is your greatest strength as a DM and/or player? What do you bring to the table that makes other people want to play with you? Do you have a knack or a talent for something in particular?
What is your greatest weakness as a DM and/or player? Is there something you continually stumble over, despite your best efforts? Is there something you struggle to implement?
Also, if you notice someone else has a weakness where you have a strength, consider giving some advice for how you accomplish what you accomplish. This is not a place for ridicule or recrimination. Criticism may be warranted, but it should be constructive criticism, helping overcome a weakness the person wants to rectify.
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My greatest strength as a DM is my ability to play fast and loose, with the dial cranked up to 11 and beyond, without it becoming cartoonish. I am quite good at running pulpy and perhaps campy adventures that still "read" as believable and grounded. Like Indiana Jones, my players' characters are often on a rollecoaster of events, with hgh dramatics and high tension.
My greatest weakness is coming up with compelling BBEGs and their nefarious plots. I struggle to create BBEGs who are even believable to me, and I struggle finding the BBEGs motivation for the nefarious deeds they try to pull. Thus, my players don't engage with my BBEGs, and my campaigns end up being more "freak of the week" style plots.
As a player, my greatest strength is adapting my character concept to how the campaign evolves. One of my greatest frustrations as a DM (and as a player, too) is another player saying, in essence, "My character isn't going to bite the hook you've baited." We're all here to play, so I do my best to find an excuse to go on the adventure, even if it means refining my concept for my character on the fly.
My greatest weakness as a player is my ability to speak with my character's voice. I'm good at understanding my character's wants and needs, and I can act like my chacterr, but speaking like my character is hard for me. I don't mean stuff like accents (that part is easy). I mean the manner of speech and colloqialisms and turns of phrase that people use that define how they sound. All my characters end up sounding a lot like me, but with a funny accent. It's not so bad on PbP (because I have more time to craft my words), but in person? Phbbbt.
My greatest strength as a DM is my improvisational ability. I can put together different ideas in ways that make sense and that are interesting almost instantly. I'm good at drawing ideas out of other people at the table and getting them to work together and collaborate. On the fly, I can create compelling situations with clever challenges that "scream" the theme and tropes we're going for. My villains loom large and my locations are full of depth and history despite being sometimes created on the spot. I'm good at teasing out potential angles of the emergent fiction to exploit and use to fill the characters' lives with adventure. When I prep (and I prep a lot even if I throw it out in favor of a player's idea), it's very detailed and generally visually stimulating. When I adjudicate, it's fair and balanced with collaboration with the player where needed to make sure everyone's onboard with the stakes.
My greatest strength as a player is also my improvisational ability. I'm always ready to go with an action or bit of dialogue that fits the scene well. As well, my characterization is on my sleeve from the word go - you will know who my character is and what he or she is about right away because I will show you by my actions rather than just tell you. I also do not block other players. If they want to do something, I back their play and add onto their ideas, never negating or denying. I will never hang around and debate the issue or say "No." I establish bonds with other characters quickly by latching onto some element of the other character I find compelling. I use my control over my character to put myself into interesting situations, even if it's not the smartest thing to do game-wise if it makes for a better story. As a player, I try to get more done before the pizza arrives than some people do in an entire session. If people aren't talking about my character long after the game has ended, I failed. (And failure is not an option.)
My great weakness? I'm too humble.
My strength as a DM is improvisational as well, with a specialty in player generated content (player ideas that become entire subplots).
My weakness as a DM is herding cats. I just cannot direct and keep the players on track and focused. I have one of my current players help me in this regard.
My greatest strength as a player is combat trivialization. Really it is rapidly becoming the specialization of my entire current gaming group. Defeating encounters designed for characters of much higher level is becoming frighteningly common.
My greatest weakness as a player is harder to describe. "Normal" characters simply do not intrigue me. I need either an unusual class/build or an unusual race to get me interested in a charater/game. I could never play at a "Core 4" focused table.
I not sure I know my greatest strength or weakness, but another DM I had played with for many years was very good at having the campaign prepared down to very minute details, like having every encounter or room populated with objects, history, etc. But the DM was reluctant to do things on the fly, or allow the players some room to breath when fleshing out their characters or performing ad-hoc actions.
My greatest strength as a DM is that my playstyle is well suited for the people I run games for.
My greatest weakness as a DM is that my playstyle is not well suited for the people I do not run games for.
My greatest strength as a player is that I contribute positively to the style of game I enjoy playing.
My greatest weakness as a player is that I do not contribute positively to the style of game I do not enjoy playing.
My apparent strength as DM is flexibility. So far the unexpected hasn't left me flat-footed.
My biggest weakness as DM is details. I'm still working on my narrative voice, so my descriptions tend to bounce between over-wrought and bare-bones-to-insufficient.
My biggest strength as a player is being a team player. I like to do my thing, but I also like to make sure everyone has a chance to do something awesome. I love set-em-up, knock-em-down tactics.
My biggest weakness as a player is greed. I want my fair share, and then some when it comes to the special treasures. Shouting dibs on the first magic sword we see, when there are at least three other party members who could use it, and I just had a weapon upgrade... and don't normally use swords in the first place.
Interesting topic.
I guess my greatest strength as a DM is that I'm pretty good at improvising for whatever the players decide to do. If everyone decides to go over there suddenly, then I can figure out what's going on over there before the characters actually arrive. (A random encounter is usually sufficient to buy time.)
My greatest weakness is that I don't have an eye for details. Since I know the players are going to ignore the various ornamentations and rugs in a room, I've never gotten very good at coming up with that stuff on the fly.
I'm also pretty good at presenting options neutrally, without projecting any sort of bias about what the players should do, with the side-effect that sometimes the players aren't sure about what to do next. I'm not very good at railroading, even when it might be helpful.
My strengths are
Creating creative immersive living worlds that have NPCs that resonate with flavor.
Having a great depth of experience at adjudication that I can be fair and even handed without showing bias.
Multiple plot creation that creates a lot of interest and conflict without railroading the PCs.
Good grasp of rules and rules concepts so houseruling to achieve a flavor is easy.
I manage the table and establish clear expectations well. Problem players do not tend to be long term issues.
My weaknesses are
Despite strong npc villians I suffer from dungeons that are not as detailed as I'd like. I do well by some peoples standards but I feel I can do even better.
I need to let the players stop and enjoy their success a bit more than I do sometimes but I am focusing on this and getting better.
I am hung up on maps. I am never satisfied and I am ever questing for the next good mapping program.
My greatest weakness is definitely my shyness. As a player, it often prevents me from RP'ing as in-depth as I'd like to. And, as a DM, it keeps me from exploring some of the more interesting avenues of campaigns and adventures that I would otherwise jump at. It generally takes me about 3-6 months of hanging out with someone twice a week to get over that. Of course, it also makes me less likely to get into a group to begin with.
My greatest strength isn't really one thing as a DM, but rather a generally strong expertise in most aspects of the game. My campaigns are A+ and could be written as screenplays that would be better than what Hollywood comes up with, and my storytelling is a solid B+. I'm proficient in controlling the game flow and ensuring the players have fun with a sense of freedom in their actions. I can adjust to my players unexpected actions and not miss a beat, just making it up as I go along and do so smoothly as if everything they did had been planned for months while still goving them the feeling that they "got one over on me." I know when to cling to rules, and when to break from them. I know when to put my foot down on a ruling, and when to concede to a player's arguement. Playesr neither feel like they could survive anything, nor that I'm "out to get them." I run a tough game, but if you died, you did something stupid or things just went unavoidably sideways.
I'm not sure I would give myself a 5/5 overall, and I know at least one DM who exceeds my expertise in storytelling as he can make you feel you are actually in a room he's describing like nobody else I've ever met, but I really would give myself a 4 or 4.5/5 in every aspect of the game. The downside of being good at it is that the players always want me to run, but that has given me a solid 25 years of experience in DMing. I suppose anyone could get good at anything with that much time under his belt. Were this a career I'd be looking towards retirement at this point!
D&D should come with a pension. 
I will say that I have a very irritating deficiency as a player that I, to my credit, do my best to supress. I have an idea of the "right way" to DM, and when I feel as though someone is DMing "wrong" I fight with my inner demons to keep myself from saying so and trying to correct them. I need to lean a bit more tolerance to allow for varying styles of running things.