I'm not sure if you understand the background on this. If the following is stuff you already know, sorry.
In American schools, if a student is involved in some legitimate educational activity that will result in him being late for a class, the teacher supervising that activity will give him a "late slip", that is, a piece of paper stating that he is late for a legitimate educational reason and not because he was just hanging out with his friends or something. For example, if the teacher of class A keeps a student after class to discuss an assignment, and this makes him late getting to class B, the teacher will give him a "late slip".
Normally students are not allowed to wander the halls during class time. A student is expected to be in class or in an area designated for breaks, like the lunch room. A teacher can authorize a student to be out of class, perhaps to run some errand for the teacher, by giving him a "hall pass".
So the sentences you quote are metaphors. The speaker is saying that when his friends failed to show up for things they planned to do together, he would "give them a late slip", that is, he would ignore their lack of consideration. It is likely that is intent is not just people being late for a planned activity, but any sort of failure to act as a friend.
Likewise, when he himself broke a promise, he gave himself a "hall pass", i.e. he made excuses or forgave himself.