Some Midwesterners and many speakers in the Eastern States pronounce cot and caught as /kɑːt/ and /kɒːt/. (Pronunciation and spelling information from Handschuh and de Geigel, Improving Oral Communication (1985)) Speakers who pronounce both types of words with the vowel /ɑː/ might not hear a difference and might not know why Midwesterners misunderstand them.
As there is no stigmatization about which is right or wrong (unlike r dropping which is seen as nonstandard in American English), you can choose whether or not to make a distinction. If you want to make the distinction, the following guidelines will be useful.
1. /ɑː/ is represented in writing by:
• a: in most stressed syllables followed by r or r + consonant: far, army, card, farther
• o: as in odd, lock, mob, doll
Note: words in which o is followed by double r may be pronounced /ɑː/ or /ɒː/: sorry, tomorrow
2. The following combination of letters are almost always pronounced /ɒː/ in the Midwestern dialect:
• consonant + o + ss: boss, loss, toss
• consonant + a + ll: ball, call, tall
• consonant + au: sauce
• consonant + aw: lawn
• all other past forms ending in ought, aught, such as fought, cought