This will not work fully with Love 0.10.1, you'll need the development version.
ctrl+z,x,c,v do what you expect, for the most part.
ctrl+d deletes the selected object.
ctrl+g toggles the grid.
ctrl+b or ctrl+click a shape to select the body instead of the fixture. When a body is selected, drawing more shapes will attach them to that body rather than creating a new body.
Hold alt when drawing a shape to snap to grid. Hold shift to draw around a point.
Hold ctrl when drawing a joint to collide connected bodies.
Roll mouse wheel to zoom, press it to pan.
Right click to finish drawing chains and polygons.
Known issues:
All joints available except mouse and gear. There's no "world body" yet so some joints are not really useful, like wheel. Keyboard commands not mac-friendly. Undo stack not constrained, but I haven't run out of memory yet

There is also at least one thing that can't be serialized properly at the moment (reference angle for some joints, #1194). This affects the undo stack and save/load behavior. Thanks to bartbes and slime, many similar issues (#1175, #1176, #1179, and #1191) have now been addressed; I'm looking forward to seeing these in the next Love release.
If you find an issue that wasn't mentioned above, please let me know. Also, any suggestions for improving user input are welcome.