I know you asked this question a while back, but in case you are still wondering, thought I put in my two cents as well.....
As others have said, the smell comes from the sea grass that washes ashore on the beach on Padre Island and in Flour Bluff simply due to the direction of the water currents. The smell comes from the plant material decaying and it does smell worse in the summer when the sun is baking it all day.
The water currents and weather determine when it washes up and how much there is. It varies based on these factors, but there is always going to be some certain times of the year due to the currents. The currents change in the fall and there is usually a lot less to none, unless there has been a storm.
Nearly all beaches deal with seaweed to some degree. When you live on the coast you find this out. When you visit a resort the machines were at the beach before you woke up scraping it all up for you!
I have lived in Flour Bluff for two years and just bought a lot in the bluff on the water and can tell you I have gotten used to the smell. As others have said, it doesn't smell all the time (or even most the time IMHO) and that also has to do with wind direction on any given day.
Regarding the mucky shoreline and getting in the water....The Laguna Madre is different than the ocean. The shore is a mix of sand and mud and decayed seaweed, so it will be mucky along the shore in most spots. Not that many people really "swim" in the Laguna Madre. If you go out in a kayak or a boat you can easily find what's called "pot holes" which are large open areas with a sandy bottom. I personally think those are great places to swim especially on those days when the water is crystal clear (also caused by the currents and wind). You can break out the snorkle mask and have a great time.