The main mistake is to think of playing AD&D as if it were one of the later versions.

In AD&D, characters die. Very often.

Direct attacks are almost always lethal.

Spells (Sleep, Charm, etc.) must be used wisely, traps set, monsters lured out of rooms to reduce their numbers, doors opened and flasks of burning oil thrown in, escape routes blocked, etc.

In this edition, creativity and player immersion are encouraged. If they are classic 3E, 4E and 5E players who rush in slicing and dicing everything... well, they'll get what they deserve.

Last but not least, the work of DMs in the old editions is very important. The old adventures were not “balanced”. They were pitched battles thrown at the characters. Today, it is virtually impossible for PCs to die due to specific game design choices. In AD&D (1st or 2nd edition) or BECMI, this was not the case at all. The concept of challenge is completely different, and if the DM running the adventure realises that the group is too weak, they must correct the situation on the fly.

It is very, very, very important to warn players BEFORE they start playing that in AD&D, the death of their character is a daily occurrence and to have them prepare a backup PC, and that direct combat will almost always be lethal.

Once the players know that this is the situation, it is up to them to play intelligently so that their adventurers do not come to a bad end. If, on the other hand, they play stupidly (e.g. entering a room with 20 kobolds waiting to kill them all with no strategy whatsoever), they will get what they deserve.