In some ways it does, potentially, open up the possibility of problems from one application from affecting others.
But, full trust is actually pretty safe by default already, especially from external attacks. The biggest risks in full trust scenarios are from the legitimate users who could, possibly, upload and run code that does something stupid. Again though, this is a minor risk in overall practice, which is why you see hosting with full trust at all.
Hosting providers also do a few things besides to further reduce the effects of one errant user's idiocy. Most of the providers do make a few tweaks to the "full trust" defaults to eliminate features that asp..net solutions wouldn't actually need anyway. They also tend to run each user's account in separate app pools on the server too.
Also, there were some problems with the default medium trust settings that resulted in full trust being very difficult to achieve with many asp.net applications. Microsoft has made some changes to how code access security and trust levels work in asp.net 4.0 to address these concerns. I haven't dug into the final details myself yet, but you can find a bit of information on them at these links:
Security Changes in the .NET Framework 4
Code Access Security in ASP.NET 4 Applications