Jam are borderline post-punk I think. This is a genre where the lines are pretty arbitrary I think (although I guess that's true of most of them).
PiL are unlistenable garbage in my book but they're important to the genre so I guess you can't really leave them off.
Same with Joy Division, though they're slightly better. I wouldn't have both JD albums though.
First Cure album strikes me as inessential but I think it's fun enough.
Gang of Four aren't really my thing but I get why people like them. I think of The Pop Group as a worse version, can't remember if that's accurate except I just know I didn't like them.
The Raincoats, Au Pairs, Kleenex/Liliput, Bush Tetras, Delta 5 - there's a bunch of these I kind of all lump together. I think the Au Pairs' album is the best of these, followed by Kleenex/Liliput. Have never liked Raincoats much but they're fine, and definitely influential.
The Feelies - Crazy Rhythms. For some reason I don't really think of them in this genre. I guess they should count though. This album's good although I never listen to it.
U2-Boy. I forgot about this one - sure. I probably wouldn't include their later ones.
The Fall. I picked Slates but it's an EP which maybe you prefer not to use. I don't know if I've heard Perverted By Language but the other three you mention are all good though I think Hex is a bit overrated (or maybe I just think "And This Day" is annoying). My inclination would be This Nation's Saving Grace if I had to pick one and add either Grotesque or Dragnet if you want another (I think I prefer the latter but not by much).
I don't think Sandinista is post punk but even if it was, I don't think it's near being one of the 25 or whatever best/most essential albums of the genre. If this counts, so does the second Specials album which is much better.
Mission of Burma. Again, Signals, Calls, and Marches is an EP, but it's a great album and Vs. is at best a pretty good one. I'd go with Signals.
This Heat, Flipper, Echo & the Bunnymen, Throwing Muses, Essential Logic - bands I've been vaguely meaning to listen to more than I have
I don't have enough data to support my view that nothing Nick Cave has ever done is good, but that's just how I feel.
I think if Feelies count as post-punk then so do Dream Syndicate, but I don't think the Dream Syndicate album is all that good.
ESG. Vaguely important but not actually good to listen to. See also Liquid Liquid, who are in a similar space. I'd probably include Contortions over either but I'd much rather have either of Cristina's first two albums for that mutant disco-funk thing.
I like Psychocandy but I'd put it in wherever the shoegaze stuff is.
The Sugarcubes-Life's Too Good. I love Bjork, but I don't like this. Don't really like Swell Maps either.
Rapture, Savages, Iceage. Haven't heard much of any of these. I think this is a list where I'd probably stick to a time period, but if you wanted to include something modern, I'd probably do the first LCD Soundsystem album.
Tuxedomoon - Desire. I thought Half-Mute was kinda neat, but I can't remember if I've heard this one.
XTC - I think an XTC album on such a list would make sense, but I couldn't tell you which one.
The Golden Palominos - s/t. I know some of their later albums but this is supposed to be totally different. Would fit into the Contortions/ESG group so if it's good, ditch those other ones.
The Soft Boys - Underwater Moonlight. Doesn't totally fit into the "postpunk" category in my head, for whatever reason. It's alright, but I'd probably rather listen to "I Wanna Destroy You" and "Queen of Eyes" five times in a row each than play the whole thing.
Tom Verlaine - meh
Some other stuff to consider:
The Gun Club (taught Jack White everything he knows)
Art Of Noise/My Life In The Bush Of Ghosts - probably most people wouldn't count them as postpunk, but you could
Devo - maybe people put them in new wave, but that feels wrong to me
Bauhaus, Sisters Of Mercy (assuming you're not making a goth section). Though I think I prefer Love And Rockets to Bauhaus (much like I prefer New Order to Joy Division)
Dead Can Dance
Half Man Half Biscuit
Midnight Oil - Head First
The Teardrop Explodes
Throbbing Gristle/Cabaret Voltaire. I confuse them besides knowing that I don't like them, but I think both were influential.