After 20 some years of hosting martins you can still learn valuable things.
Last year I had a nest with mud smeared eggs. They did not go to completion. A re-nesting occurred once I removed them, but that was after 3 weeks
This year, a very wet one, I had 4 nests with muddy eggs. The 2 that were slightly dirty hatched. Another nest hatched 3 of 4 eggs. The remaining nest is a loss.
What I believe is that in an active nest the parent bird is constantly turning the eggs. This cleans most of the mud smears off. So there is hope for slightly mud smeared eggs. But if they are very dirty, they are likely dead eggs. (Wish I had pictures to show "very dirty" to "slightly dirty, but it is obvious when you see it)