I have the same problem on my website, the error 35 and the unexpected problem errors shows up for every plugin that I want to update and when I tried to install a new plugin
My first thought was maybe I made an error using wordfench to delete some files it found in its scan so I used a back up to return my site to a version before I let wordfench delete the files but this did not work.
After I used the backup my site was on an older version of WordPress. When I tried updating WordPress I got the error 56.
I did notice. When I keep trying over and over to update or install new plugins eventually one of the tries will work but this is extremely annoying.
Is this a problem with WordPress or is there an issue with my web host server?