The place I used to work used an access database for thier contact management system and it certainly had problems when more than 10 connections were made to it, that may have been that it was poor written in the first place or a whole host of other reasons by since then i have also heard from others that they've have problems with access when using more than 10 connections.
As for mysql I think alot of the negativity is from the older days when some features such as enforced references(i think) and stored procedures weren't available. If you check out who they say uses mysql (
http://www.mysql.com/customers/) its an impressive list including yahoo, French Ministry of Defense,
and google, although im not sure what they are using the database for!