Did I do a shoddy wiring job on a ceiling fan?
To answer your concerns:

The reason the National Electric Code requires wires to be contained in an approved enclosure/box is to protect them from being damaged, but also for any arcing that might occur (the resulting spark and heat are restricted inside the box. From experience having installed more than 15 ceiling fans: wires should be no shorter than 4 inches exiting a box, wire them in this order grounds, whites and hot last; this is also how they should be placed back into a box. If the box is full with other wires unrelated to the fan I will try to at least push the wire nuts into the enclosure and tuck the leftovers out of the way.

Also, for your own peace of mind, try this: after tightening a wire nut give the wire a gentle tug. If it doesn't pull free it most likely will remain so. For even more peace of mind (and because its mama's) wrap the wire nuts with a few turns of vinyl electricians tape in the same direction that the wire nut was tightened. I would double check your work since you expressed concern (and because it's your mom). As long as you have sound wire connections and the box is rated to support the fan you will be fine.