EDIT Dear User, this is just to tell you that I have trimmed a bit the Google list. It contains all the solutions to the AM exercises I have been able to find on the web, but I'm sure there are many others. If you know some of these others, please add them to this community wiki answer by editing it. TIDE
This is not an answer, and this is a community wiki.
I don't know if it's a good idea, but if you're interested you can help me collect here links to online solutions to Atiyah-MacDonald exercises.
Here is my Google list of such links.
It's very messy, and some links are broken.
If it turn out to be a bad idea, I can delete this "answer", and give the link in a comment.
Here is a MathOveflow Errata for Atiyah-MacDonald.