Basically anything that has a special ability can be annoying, but then again it's rather the point, else you'd be fighting fleetballs all the time.
The main problems I had was "stupid" OP combos like shield + drone spawner, shield + tractors, shield + swallowing.
Or gravity effect with any kind of kiting ships in front, or gravity effect plus any kind of long range (from drone spawners to snipers). Gravity immune ships on gravity worlds.
Anything that becomes a doomball in high number too I'll count as annoying / broken. The neinzul thingy that replicates each time it hits for example (forgot the name...). It's basically 5 times faster than anything you have and will replicate / tank your fleet just before it transforms it into scrap metal. Only sensible way to kill it is throwing immune stuff at it, which is a complete no-go for me in term of design. Droneships are included here, but more due to large battlefields and slow moving speed. Once caught-up they're fine, its just that they're so annoying to catch when under a forcefield on the other side of a map with a gravitic station...
Another thing I found particularly annoying is space planes... but they're gone.
Battlefield wide effects are also major annoyances, like battlefield wide EMP, gravity, planetary anti-cloak, ion cannons... a few others, probably, which I forget, because of the combos there is. Complete EMP + replicating ship is basically doom. Anything battlefield wide means snipers / droneships own the place.