Mono implements the 2 ECMA standards related to the C# language, the CLR and the core of the .NET library, plus Microsoft-specific APIs which are not covered by the ECMA standard.
The ECMA standards are distributed under RAND terms. This is not enough to guarantee a free implementation, however Microsoft issued a statement under the Community Promise that these standards are worry-free of patents as long as the implementation implements the whole standard (which is quite light and contrary to Java, supersets are allowed).
What can be attacked are implementations of components, like ASP.NET, ADO.NET, Windows.Forms and maybe Silverlight. However, this would be a hard thing to do, simply because Microsoft ended up cooperating with the Mono team on at least the implementation of Silverlight. And also they actively encouraged Mono by other things, like referring to Mono in their official docs, which means Estoppel applies: http://en.wikipedia.org/wiki/Estoppel
So quite the contrary, I think Mono is even safer than Java, as Java is not governed by a real standards body and you can't implement Java unless Oracle allows you to (hence Harmony is dead). Even forking OpenJDK may be problematic, as the implicit patents grant may not apply to derivate works (at least in Europe).
There have been software patents in the EU for decades. The section on "Europe" in the Wikipedia article on software patents (http://en.wikipedia.org/wiki/Software_patent) contains links to decent explanations of what's going on there.
It's not as "bad" as the situation in the US, but software patents have been issued in the EU for decades. The question of which software patents are actually valid and enforceable has been giving everyone a headache for just as long.
The European Patent Convention is somewhat ambiguous in its effort to both ban pure software patents, and permit some things that we might think of as software patents, meanwhile each country puts its own unique spin on the issue (the European patent system is not as unified as people sometimes expect), and courts do not always behave consistently.
In a way, it's an even bigger mess than we have in the US, the mess just doesn't get dropped in burning paper bags on doorsteps quite as much.