Sometimes when i order my guys to move to a location right in front of them or shoot someone, they will attempt to do extremely stupid things, like try to get there by circling the block in the opposite direction or run up to them and hump them without using their firearm.

is this because they have very low intelligence, or is the game just incredibly glitchy? i have only managed to get him to shoot once, in self defense. he has one and a half stars of intelligence and maximum firearms skill, and the one time i got him to shoot he killed 4 cops in 4 shots. but i cannot make him shoot on demand. he just runs up to the people i order him to kill.

also i have found that some of my lieutenants simply fail to follow their orders. their underlings will carry out their assigned tasks, but the lieutenant will just fail to leave the office. do i need to kill these lieutenants, or is this just a glitch?

well, im not sure i entirely understand why it works this way, but i have found that if i break the group down into 2 smaller groups then they all follow their orders.

and it seems like 2 and a half stars is the minimum intelligence required to make people shoot on command.

if your hoods are out numbered or possibly a cop is in the immediate vicinity they will just say uh-oh they just want to live through he week and really aren't up for suicide missions. Pair up your Patrols and have them close enough to back each other up .
I also remember that shooting from a certain distance when a rival passes you(shooting them in the back) seems to work better than when they are looking at you.
as far as your lieutenants they need to be organised and intelligent then have certain traits to work in the gang. Always give individual orders to each man especially collecting protection money. not sending out your lieutenants is a good option as their deaths really through a wrench into things if you really need them Keep them close to your HQ. you can repeat orders for a lot of things unfortunately recruiting you cant
also the order which you send guys out is important collection and recruiting need to be on the top of the list if they are on the Bottom they will start much later than the first group. There are ways to work around that in the game, getting everyone to come out beginning of Monday morning