<p>How solid is Mono for C# development on Linux and OS X?  I've been thinking about learning C# on the side, and was wondering if learning using Mono would suffice.</p>

It should be just fine. It supports C# 3.0 now. I usually try to stick with targeting 2.0 though and it is very stable.
Winforms and ASP.NET have both worked fine for me. The only thing to consider is there is currently no support for WPF.