Long list here, not sure what to exclude/include, but here goes:
Excess chainline dimension and/or wasted space between freewheel and dropout (which is sometimes necessitated by derailer claw hardware).
Related: The modern crankset, having a fixed spindle length, but preceded by Octalink bottom brackets having few if any length options.
The problem being a radically crossed chain when using the big ring with the bigger end of the cassette.
Tight-radius handlebar drops like cinelli Giro model 64. Causes me hand pain by means of a pinching action like a rough handshake.
Bulky modern stems on a traditional steel frame. JUST-LOOKS-AWFUL (to me).
Saddles with narrow and/or hard nose area. Makes me prefer only the shortest rides. The saddle makers have responded as of late, hurrah!
Seatposts with sticking adjusting hardware that has to be impacted in order to make a fine adjustment to the saddle tilt (clamped barrel-type cradles et all).
Not usually a vintage concern, but q-r seatpost clamps together with a post that falls freely into the seat tube. Maddening!
Vintage wheelsets on a bike I've bought, where a shop has replaced a rim and had to use 36 14g spokes to save a few bucks on inventory or possibly at the cheap owner's request (not that the rim mismatch isn't usually even worse!).
Rims with narrowest brake tracks, like HED Belgium (or Ardennes complete wheelset).
Over-packed hub bearings, as if the bike was going under water.
Seat bags with stuff jingling inside (I don't use seat bags on the road).
Modern bikes where running the cable housings through the bars and the frame seems to take several hours.
Modern derailers that mangle the cable at the pinch bolt. It's like they've suddenly regressed 60 years to the days of Allvit derailers and cheap brake calipers.
People's insistence on cleaning chains with solvent (I lube and wipe only).
Related: Over-lubricated chains.
Outsized Jagwire housing ferrules, intended as advertising flags, but often sit crooked, look gaudy and don't belong on my bike.
Related: Shimano's largest-cog color and graphics, yuck!
Front brake cable hanger noodles with a sharp bend. Look like box-store design quality exactly (and even worse with no plastic liner).
Heavy steel reflector brackets. Did these really need to be as strong as a crankarm?
Vintage rear derailers featuring too much of a chain gap distance for use with flexible modern chain (even with any b-tension screw removed).
Any component that requires special, rare and/or expensive tools to service and/or install or remove.
Any freewheel that can hit a false neutral and "skate the chain", even if only occasionally.
The difficulty in finding clipless pedals for 1/2"-threaded, one-piece cranks (I got mine, eventually).
SRAM and Shimano's wonderful 12-32t 7-speed cassettes,
not being available as freewheels! (12-14-16-18-21-25-32t). Thirty million box-store bikes be needing these too.
The old split-tip freewheel cogs
not being available in cassette form, ...
NOT.
Leg cramps while sitting down enjoying post-ride coffee.
And (just so that I don't leave this thread all grumpy), here are a few things that I don't mind:
Wrapping bars bottom to top (I always wrap bottom to top).
Safety levers
Stem shifters
Pants guard ring
The blessings of modern chain, even though some vintage components don't always get along with them in every situation without modification.
Components that require special tools (but are tools that I already have, lol).
.