Is a 3/8 "romex" connector listed to be used with a combination of a 12-2 and a 14-2 NM running through it? I believe that it has to be two 12-2's or two 14-2's (no mixing of different sized cables allowed). Of course other single cables can also be inserted.
This is one of those things that if it looks OK it is probably OK. When you see the other listed Romex clamps (buttons and the internal clamps in blue NM boxes etc, these old style connectors look bulletproof. If the jackets all got in there undamaged and they are well secured, what would the problem be?
You would definitely want to check the connector manufacturers literature. I know that the Arlington #814, which is a basic two screw 3/8"[1/2"KO] NM connector I often use, is listed for a bunch of different cable combinations, some of which I would not usually consider using, like two 14/2 and one 12/3 in the same connector. I stock some other two-screw connectors made by Topaz that are rated basically the same.
Even the Arlington "black button" plastic 3/8" NM connectors can be used with two 14/3 or two 12/3 cables, and both the T&B and Arlington's plastic push in "wedge lock" style connectors are rated for many different cable combinations as well. These wedge lock connectors are also rated for use with flexible cords within a certain range of diameter.
It gets a little ridiculous with some of the larger size plastic NM connectors, like the 1" and 1-1/4" where they are rated for use with up to nine 14/2 or ten 12/2 as well as several other cable combinations.
Years ago when I worked with my old boss, we use to install two 14-2 RX wires in one 3/8" connector. Some AHJ's would allow it and others wouldn't. they were never listed for more than 1 wire, but 2 wires would fit in there with no problem. This might be where the AHJ uses 90.4 of the NEC. There was a proper two wire RX connector which you could install two 14-2 wires,14-3,12-2 or 12-3 wires. The newer plastic connectors ( I believe) are listed for multiple wire connections.