I use wire nuts just about every day in my day job. The comments about the size wire nut MUST be sized to the gauge of wire, and *how many* wires you're trying to put under the same wire nut are spot on. The other issue with using wire nuts is all the wires must be stripped to the same correct length for the nut. Then getting all the wires lined up so their tips are even with each other, you can't have one wire sticking out further, or one wire hanging back in the bunch. Then after twisting the nut onto the wires until it is tight, you MUST tug-test each of the wires under the nut to make sure none of them are loose and pull free.
I use the Ideal brand wire nuts most of the time. And that's because I've had good luck with them. Most of the wires that I deal with are 12 ga and under (smaller). On the 20 ga and smaller wire, I prefer Scotch-Locks over wire nuts. They are a gel filled snap-crimp style connector that is/was heavily used in the telephone industry.
Done correctly, wire nuts will never loosen up. Even cramming them into a J-box. But J-boxes have a similar rule to wire nuts. The J-box MUST be sized to how many wires (and wire nuts) you are trying to cram into it. I see more electricians violating this "rule" than just about anything else out there (more so than the "pipe fill" rules about how many wires you can fit in a conduit). You can always add an extension ring to a J-box if the wires won't fit. Most electricians will just try their hardest to cram and overstuff a J-box so they don't have to go get an extension ring.