From working in this forum for quite a while, I have seen quite a few scenarios where folks run into problems:
Leaving a fish at the LFS for a month to make sure it has no parasites. While this seems to be intuitive, there are several problems with this. First, many local fish sellers run copper in their system and this will mask various parasites. Secondly, since LFS run fish systems, and receive new fish frequently, they are constantly exposing fish to new parasites and other diseases. And third, but more important, parasites are not obviously visible until later in the life cycle.
Buying fish from local reefers is the safest. While this too seems obvious, what you don't know is when the last un-quarantined wet item was added to the local reefer's tank.
I quarantined the fish for three weeks before adding it to my display tank. First, that is not long enough, and secondly, as mentioned above visible signs of a parasite come at the latter parts of the life cycle.a If purchased from an LFS that runs copper, parasites tend to show up around the fourth week after being removed from copper.
My LFS keeps their fish at hyposalinity, 1.016, so they cannot have ich. Several problems with this one. First, 1.016 is not hyposalinity even thought the SG is lower than Natural Sea Water (1.025) and LFS do this to save on salt not to cure ich. What is worse, hyposalinity, even if 1.008/1.009 which would cure most varieties of ich (but not all), has no effect on brook, uronema, or velvet.
I always give my fish a fresh water dip before adding them to the display tank. This is stressful for a fish. While it can be used to diagnose flukes, it has no effect on ich, and only a temporary effect on velvet.
Hope this dispels some of the ideas some folks have about fish parasites.