What affect does the permutation layer have on the avalanche effect? If the permutation is not well thought out, how will this effect the cipher's avalanche effect. For example, if the permutation in PRESENT was in some way different (just made up without any thought) would this adversely affect the avalanche effect? How else might a poorly designed permutation adversely affect PRESENT or other block ciphers?
Permutation layer diffuses the small changes globally(tries to spread over the complete block). 

If permutation is not well thought out, then diffusion may be weak and changes may not spread throughout the complete block. The cipher output may be treated as concatenation of output from multiple identical ciphers with smaller block length. For Example 

Consider there is no Shift-Rows operation in AES, then Change in a state will stay in a Column and will not diffuse to other columns. Thus Ciphertext can be treated as output of 4 independent 32 bit block ciphers.

In Case of PRESENT, if the permutation P was not spread over the complete block(64 bits, keeping the change within small set of bits), or there was a chunk of bits which does not get effected by change in other bits over multiple rounds, the cipher will have a major weakness.