I know this is a novice question, but my sandboxed solution works on one site and not the other. How/where can I actually see the errors generated by some sort of report? Debugging simply takes me to the site where I can see that nothing is actually happening although the solution has been deployed.
Use the developer dashboard for debugging your sandbox solution:
The Developer Dashboard is an instrumentation framework introduced in Microsoft SharePoint Foundation 2010. Similar in concept to ASP.NET page tracing, it provides diagnostic information that can help a developer or system administrator troubleshoot problems with page components that would otherwise be very difficult to isolate.
More info, including how to turn it on/off via powershell here.