Jamieson, Fausset and Brown on Jeremiah 38:6

6. dungeon--literally, the "cistern." It was not a subterranean prison as that in Jonathan's house (Jr 37:15), but a pit or cistern, which had been full of water, but was emptied of it during the siege, so that only "mire" remained. Such empty cisterns were often used as prisons (Zec 9:11); the depth forbade hope of escape.

Hammelech--(Jr 36:26). His son followed in the father's steps, a ready tool for evil.

sunk in the mire--Jeremiah herein was a type of Messiah (Psa 69:2, 14). "I sink in deep mire," &c.