This question discusses the various steps a very small gene pool could take to avoid inbreeding however most of the answers agree that it's very unlikely that a group of 6 individuals could avoid all genetic issues.
I'm interested in exactly what those issues are.
It's my understanding that most issues arising from inbreeding are as a result of family containing similar sets of DNA. We all have recessive problems in our genome, this only becomes an issue when our partners' DNA also has the same recessive issues (because two recessive defects don't have the dominant one to correct them). Inbreeding is an issue because brothers and sisters have very similar DNA and the probability of both of them having the recessive genes is far more likely than a random person.
Assuming my understanding is correct why would a group of six unrelated people have this issue? Assuming that they all have different recessive problems their children would have a chance of inheriting the same ones however they are also almost guaranteed to have the correct dominant genes from their parents!
Given that a massive proportion of genetic issues will no longer exist (because the only ones going forward will be those present in those early progenitors) why are the probabilities any higher when starting with a smaller base?
Exactly what symptoms would a colony see if it had too few founding members?