What are the identification problems in measuring peer effects? I am currently writing my bachelor thesis on peer effects. However, the more I read about the identification problems (I read e.g. Manski, Moffitt, Angrist, Goldsmith et al.), the less I understand. I particularly have a problem with understanding how endogenous selection affects my estimates (omitted variables? Selection bias?) and understanding the correlated unobservables/ related errors in variables and the endogenous membership problem and how or whether they relate to each other. 

I know this is a lot but any help is appreciated!!! Thanks a lot!!!
Well, imagine you don't know how students are grouped. Maybe better students are deliberately grouped together, for example. Then your estimation is clearly biased. You'd basically reach the conclusion that classes with better students are better. 

Peer effects are hard to identify with observational data because similarities in the behavior of peers could be due to peer effects or to selection into peer groups based on common unobserved characteristics, or to factors that affect all peers in a peer group.

To do a proper estimation we need a quasi-experiment, preferably a true experiment. Because in such context you indeed know that student allocation is random, so there's a clear causal link and possibility to separate the treatment effect from homophily and confounding factors.

Angrist and Pischke's Mostly Harmless Econometrics is a must-read for anyone interesting in working in this topic. Angrist (2014) discusses this matter in more depth and this NBER digest may help you with the intuition.