That river looks fine. There are plenty of 'endorheic' lakes like the Caspian Sea, Great Salt Lake, etc, and there are also rivers that simply spread out into an inland flood plain and evaporate like the Okavango.
The long river in the northeast though seems to be following along a raised area of hills (though it's hard to interpret without contours) Those huge lakes up in the mountains without much of a catchment area feel a bit off too.
Overall, you've got the basic idea.
As a bonus bit of criticism, you've got a problem with your projection. You seem to be using a Equidistant Cylindrical projection (Parallels are all evenly spaced and vertical distances are all to scale.) However, that would produce severe distortion at the higher latitudes.
Take a look at the map of Earth here: http://en.wikipedia.org/wiki/Equirectangular_projection
See how the parallels (Horizontal grid lines) are evenly spaced, but horizontal distance gets stretched out more and more as you move away from the equator.
Along the N 60° parallel near the top of your map, distances are only half what they are at the equator (So the map is only 3000 miles wide at 60°). And at the very top, which appears to be about N 75°, it's just a little over one quarter the width at the equator, 1553 miles wide. Even at just N 30° the map is 5196 miles wide. There's no way to have a square 6000 miles on a side on the surface of a sphere 3820 miles in radius.
Unfortunately there's no easy solution or rule of thumb. All projections cause distortion. If you are most concerned with shape, don't care much about distance, and aren't worried about the poles, Mercator is your best bet. It stretches in BOTH directions as you move away from the equator which means things tend to stay the same shape.
My recommendation would be to move the N 60° line upward and call it a Mercator map. You'd be able to retain '6000 miles' along the equator, but away from the equator the scale would change.
You can get a graticule (Grid) for a Mercator map here: http://www.cartographersguild.com/sh...ector-Template