This computer has had various distributions on, Xubuntu, Ubuntu 12.10 with a program to get rid of Unity and replace it with something similar to the Gnome2 panels and menu (gnome-session-fallback/gnome-panel?) and now Cinnamon. Probably because of its history Cinnamon doesn't work properly so I've had to use gnome-session-fallback/gnome-panel to get the classic Gnome2 panels. (I've put a separate post about this.) I think the various distributions have been using the Applications/Places menu lists, but slightly differently.
The Alacarte menu editor does not reflect what is actually on the menu. I think the menu program attempts to merge different menu lists into one. I reckon I'd be best to delete all or most of them and start again, how should I identify these files, and where should I look for them?
I've just found this page Gnome
which is well written and understandable even by a novice like me - perhaps a useful site. It suggests that they are to be found here /usr/share/applications and here ~/.local/share/applications.
I went through ~/.local/share/applications deleting duplicates and anything that didn't have a proper icon as I found that those applications weren't installed. There were about 400 files which I have reduced to 4. The menu was always very slow, now I know why, it's much faster now!