I'm not River Police, but it looks to me like there are no serious errors with the rivers. I have some minor concerns, though:
- Is that supposed to be a lake with the horizontally oriented island in it, or a section of river?
- Rivers don't flow through high ground. So that large crescent-shaped area in the top of the map with the castle in the middle (and especially around the lake) must be some fairly high ground in order for the longest river to divert its course around it. I guess the problem is that there isn't anything on the map (hills, whatever) to indicate that.
- The rivers look a bit wide for the scale of the map, but you're probably going to change that.

Other than that, everything looks fine.