Without seeing your timeline and knowing more about your procedures nobody can tell you much. The answer that is most obvious - to me, anyway - is that you used Rotobrush in all the wrong ways. seems like you used it at non-full resolution and when rendering out the result looks different.
I used it in full resolution, what can I show you to help?
I'm not sure what you are trying to do here. Your screenshots are not the same frame. Check the distance between the toe and the broom and the motion blur. We need to know your workflow and it would be very helpful if you selected the layer that is giving you problems in the timeline then pressed the U key twice so we could see what you have done to the layer. It looks to me like the actor is trying to sweep up the yellow circle and that you have some kind of mask applied to the layer. If that's the roto then the shape doesn't match up with anything in the frame so I'm not sure what's going on here. It also appears that the foot and the broom have been successfully separated from the background in the rendered frame.
Generally, if you use Rotobrush as designed, freeze the roto, and your frame rate matches the comp's frame rate everything lines up perfectly. If you don't freeze Rotobrush then anything can happen when you render. Almost always, unless the roto is only a few frames, I'll render and replace the footage before I do any other compositing. It just makes life much easier.
The shape is a puddle. What I want is the broom to rub across the puddle without showing what's underneath the puddle like it is in the second picture. In comp, it goes up and down the yellow puddle without the puddle having those holes that show the carpet. But in the exported version, it has these random holes that show up in the puddle and show the bottom layer.
Rotoscoped broom and foot
Update: Some of the puddle goes over my ankle on the left and right, that is a mistake in the comp.
Like I said, it looks like you didn't freeze the roto. If you don't do that the next time you return the CTI to the first frame Rotobrush will start to propagate and you can end up with a lot of garbage. You have to start on the first frame, proceed until there's an error, then back up to the last good frame and start again. Once the rotobrush is complete you can change to the refine edge tool and start over. When you are good all the way through the shot you need to freeze the roto, then continue with your composite.