Interesting, if I had more time I wouldn't mind trying. Sadly the best I can do is point out a few issues I see to give you something to think about.
1. River on the far right. Too long to stay so close to the shore before breaking out. Given indentations in coasts like that at Shipman's Cove are often seen as parts of valleys that extend inward from that point, I would expect the river to break out from there, not continue south. I would kind of expect at least one good sized river flowing out from the center of the map to drain that region. Even with smaller rivers that might not be shown, it seems odd they wouldn't flow together enough to warrant a spot on the map like others. Now, if there was a high fold in the bedrock, a series of large hills running along the coast that funneled the river south, rather than letting it break east, then you would be golden.
The lake in the north, seems to be fed from nothing, and flow to no where. Rivers do flow through deserts, and I can cite several cases for very dry and nearly dead looking deserts with a large river flowing through them. Extend the river north, and put a hint of green on either side of it in the desert. (Or write in the description how the river fades into the sand, and use it as some pusdo plot device.) Also add rivers flowing up from the south to feed the lake.
You have a set of large mountains in the west, and one river flowing out of them? I would suggest adding more flowing away from mountains, put the heaviest rivers on which ever side the wind would hit first on most days.