You can test the SSD using Scannerz in cursory mode. Scannerz can detect bad blocks in SSDs and identify them as bad sectors. Scannerz uses a "normal mode" that's not worth using on SSDs because it's checking for degradation of mechanical components which SSDs don't have. I don't have the company's site handy and I don't remember it, so just do a Google for "Scannerz" and you'll find it. The company now has a "How-to" section that has some articles on stuff like drives going bad, performance problems, etc. which might help you identify the spinning beach balls.
With that said, however, the SSD is supposed to be "auto correcting" these sorts of things. In other words, if it writes to a memory block in an SSD and the block is bad, it's supposed to automatically mark the block bad and not use it - or so the SSD manufacturers claim. However, I came across a post on another site where Scannerz picked up bad sectors on an SSD and the SSD didn't remap them or apparently even detect them. The owner complained to the manufacturer so they're replacing it under warranty.
As another poster said, it might be your internet connection corrupting the downloads, not the SSD. When I've done fairly large OS updates for OS X, once in a while I'll get an error when the update is opened up and checked indicating that the download was essentially corrupt. I need to re-try it and it usually (usually!!) gets downloaded all right.
Also, you seem to imply the SSD is old, and with performance problems I have to wonder if you have TRIM support enabled (or if it will even work with your SSD).
SSDs right now are a moving target that hasn't stabilized.