Thanks all for the replies.
Scaling a model up is a nice idea at first thought, but unfortunately there is not a numeric way to do this (I could easily scale a model 2.0 and then go back to 0.5, but not by dragging the mouse!).
The models in question have a lot of geometry needing to be 'merged' so doing it by hand with Weld is also not viable.
I think there should be a 'merge' and 'weld' tolerance in a future version. Shouldn't be so hard to put that in the preferences.
In the meantine, two things are helping:
1) Vertices are merged in animation frames. So, if I can make a frame in which the Merge will not 'close shut the mouth' or 'stick the fingers together', provided that I can spread the fingers apart and open the mouth by rotating the bones in that particular frame.
2) Instead of <select all> and <merge>, it's best to use the <mesh tester> in vertex mode: it will select all the vertices that are 'open meshes'. I can then MERGE them.