Nothing official. Here is a link to the page of official recalls on the 05 Cobalt.

http://www-odi.nhtsa.dot.gov/cars/problems/recalls/recallresults.cfm?start=1&SearchType=DrillDown&type=VEHICLE&year=2005&make=CHEVROLET&model=COBALT&component_id=0&TYPENUM=1&SUBMIT=RetrieveRecalls&prod_id=207911&PrintVersion=YES

I've heard a bad run of ignition switches were causing engine cut outs.
My 05 went in for a software update and an airbag miswire...

i actually have had some electrical problems. one that was just annoying and the other was kinda serious if it wasn't so specific. the one was the steering wheel mounter controls didn't work all the time and the other was that
if i was driving at night and the headlights were on and i had my foglight on and then turned on the high-beams
while the right turn signal was on the lights went out but the fog-lights stayed on. but the headlights were out. i
was like... k lol omg and actually it was a neat trick to scare my friends

and that website dosent show nonhazardous recalls so there might be others. cause the trim piece and mount for
the sunroof button was recalled cause that trim piece fell out on me and the head mechanic at the dealer i got the
car from told me that the piece was recalled so i got it fixed for free!

oh and i got the car used and the guy who had it before me beat the hell out of it and that could have been the
root of my problems