Hi Daniel and welcome to the forums.
A couple of pointers first - I never recommend link exchanges, but would rather encourage people to be more intelligent in their link approaches. Link exchanges are something that had value 10 years ago, but cannot really be recommended now.
As for checking links - the only sure way to do this really is via a link check on Yahoo search, using the following format:
linkdomain:mydomain.com -site:mydomain.com
Another couple of quick pitfalls:
1. Ensure all pages have unique page titles. Many dynamic sites can just repeat the same page title - which is effectively telling Google & co. "Hey, these might all just be versions of the same page". Not good.
Treat Googlebot as like a child with a simple level of understanding - you need to make it as clear as possible what an individual page is about, using relevant keywords on that page - so that Googlebot can take this info to the Googleplex for processing.
2. Watch out for canonical issues - simple pitfalls are to have active versions of your site running on
www.mydomain.com and non-www mydomain.com - redirect one to the other and stick to that format.
Also watch out for issues with linking to the homepage - if your domain is mydomain.com, don't link back to mydomain.com/index.html or similar index files unless there is an absolute need to, and if there is a need to, to 301 redirect to the index page from the root. The issue here is that Google does not index pages - it indexes URLs - so if you have multiple versions of a URL for the same page and actively using these, Google may be inclined to drop one as a duplicate, and kill any
advantages that the "duplicate" URLs were passing to other pages.
Hope that helps for starters.