Is it safe for a 12 gauge wire to be inserted into the 14 gauge slot on a light switch? I moved recently and was changing some light switches and noticed that several of the lights are wired this way.
Am I going to have to swap out all of these switches? These are single pole lights that have connections via both the screws and the slot being used.
That is a side clamp switch, and it's your friend. Unfortunately, whoever wired it didn't do a friendly thing.
This image is a snippet from yours:
Where that red arrow points is called a "backstab". It's quick and easy to install wires there, but, over time, the little piece of brass used as a spring clamp can wear out, leaving you with a loose connection. Loose connections lead to sparks and sparks lead to fires. Avoid backstabs at all cost.
Those green arrows point to the side clamps. You loosen the screw, strip your wire(s) bare, slip them into one or both of those little slots, then tighten down the screw. (Best bet is to use a torque screwdriver to be sure they're done properly.) Since these screws aren't under any stress, they are highly unlikely to ever back out without another application of a screwdriver and are, therefore, much more secure.
Just below where that wire enters the backstab, there should be a little rectangular slot. You can insert a small flat-blade screwdriver into that slot and wiggle the wire out. Screw it down under the clamp.
For the other wires on the other terminal, follow manassehkatz's suggestion to remove them both, pig-tail them with a 3rd piece of wire, then clamp the free end of that 3rd wire under the other screw. You can simply insert both wires into the two individual slots under the other screw and tighten them both down at the same time, but it's preferred to make a pig-tail and only have 1 connection to the switch. Either is code compliant.
In addition to what FreeMan have said, the tip of the wires seem to be wrapped in electrical tape and have exposed wiring.
You'll need to re-do these and make sure they are wrapped up after reconnecting to the switch.
No, it is not safe to do that. Depending on design, that could result in a loose connection (which can arc) or a pinched conductor (which can break).
Remove the wires, make sure the wires are not cracked (if they are and you have enough length to spare, cut off the bad part and strip a new section; if they are not long enough, upload pictures and ask a new question) and install them under the screws.
Standard switch screws can only handle one wire each. Based on the picture, you have 3 wires - hot in, hot out (to next switch or receptacle) and switched hot. Move the top backstab wire to the top screw. Get a short piece of 12 AWG black wire and wire nut it to the bottom two wires as a pigtail. Then connect the other end of the pigtail to the bottom screw.
In the early days, backstabs were made to accommodate both #14 and #12 (and it wouldn't surprise me if some recep makers even tried to authorize them for aluminum, #12 being the 15A aluminum wire). But that is gone, and I suspect UL banned it because of reliability problems.
If you note the funny business going on under the side screws, you will see this is a "Screw-and-clamp" recep, which accommodates 2 back-wires directly under the screw head (behind the front brass plate). These two are back-wired, then you torque down the screw to spec to clamp them.
The gooberhead who wired this was used to just slamming them into the backstabs and on to the next house, and probably has no idea that screw-and-clamp is even a thing :)
