I'm working right now with the book of Guillemin/Sternberg (Symplectic techniques in Physics) and there is one statement I can't prove right now.
Namely: They assume, if we have a symplectic manifold $M$ and a Lie group $G$ acting on $M$ by symplectomorphisms, that if there is a neighborhood $U$ of $G.x \in M$ such that for all $y \in U$ we have $dim (G.x) = dim (G.y)$, there exists a local cross-section for the orbits.
If we assume, that $G$ acts proper we could use the slice theorem. But it seems they claim it for general Lie groups.
Is it true? And whats the idea to prove this statement?