Example here is a multiclass Paladin 2 / Warlock 5 [edit].
Paladin 2 gets two 1st-level spell slots (via Spellcasting). He prepares Cure Wounds.
Warlock 5 gets 2 spell slots, and always casts them as 3rd level spells (via Pact Magic).
"Pact Magic" MC rules say you can Warlock slots to cast the prepared Paladin spells (i.e., Cure Wounds).
That would imply I can use all 4 spell slots for Cure Wounds (two Cure Wounds spells cast at 1st level via Paladin slots, and two Cure Wounds spells cast at 3rd level via Warlock slots). Is that true?
I understand that a pure Paladin 7 would have 7 spell slots and LoHands of 35 points (and a host of other cool features). That's great for burst healing. But given that the warlock can regain 2 spell slots every short rest, this provides this MC character a significant amount of healing output over time (provided there is time to rest) as well as cast higher level Cure Wound spells (3rd) than a pure Paladin 7 (two 2nd).
Our group already has another character acting as pure healer, but we're lacking arcane entirely. So I'm just curious how this kind of MC paladin/warlock might be very cool to fill a few different roles all at once; backup healer (over multiple short rests), plate+shield front line, protection fighting style, War Caster eldritch blasts, melee (either thirsting blade or paladin 2nd attack, lifedrinker, hex), nice ranged attack paladin lacks for those situations, counterspell spell & Mage Slayer feat, and some neat utility warlock spells. Considering Paladin 2/Warlock 18, or Paladin 6/Warlock 14 (for aura of protection).
Anyone play around with this yet?
I'm a bit confused because you start out saying you're Paladin 2/Warlock 3, but your example is Paladin 2/Warlock 5. I am assuming the 7th-level example is correct.
Assuming you're seventh level, and the slots at those level are as you say they are (I haven't checked) then yes, that is correct. And you get the Warlock slots back every short rest too.
Which means basically your analysis is quite correct, at least in theory. I don't know how useful the character will wind up being in actual play.
Paladin X/Warlock 3 is pretty good. In addition to what you just described you can also get shilleilagh from Pact of the Tome as a Warlock spell and use a quarterstaff with your Charisma modifier.
I'm intending to make a Paladin 11/Warlock 9 (eventually) that uses a glaive, supplemented with a handful of spells. The paladin armor proficiency level 5 extra attack are very nice complements to a Pact Blade warlock, but I'm getting the impression that my build specifically won't really come into its own until level 10 or so, and even then it may not be 'competitive' with other builds. It looks like a lot of fun to play, though.
As I was looking at possible level splits, I figured that most of the Mystic Arcanum bonuses for higher warlock levels weren't nearly as desirable as an extra 1d8 damage on every melee attack from Paladin's Improved Divine Smite at level 11. Just something to consider when you're looking it over.
Interesting. Thank you all for taking the time to respond.
I suspect the player will say that Lifedrinker (invocation for warlock 12) is a "good enough" replacement for Improved Divine Smite. Plus, by going beyond warlock 9, you can get 3 or 4 warlock spell slots per rest, 3 or 4 beams with eldritch blast, more spells know, more invocations, patron features and the Mystic Arcanums. That seems like a decent number of features.
That's obviously your call to make. I do agree that Lifedrinker weighs considerably in balancing the equation out. I think I ended up disregarding it because it didn't fit the character, so if you're taking Lifedrinker, you're probably good to go. Charisma damage on every swing will probably outmatch an extra d8 of damage 
I will say that you should be getting the full benefit of Eldritch Blast's level increase no matter how you split the levels; it appears to be based on character level rather than warlock or caster level.