You might find that the corners of your image get shaded by stacking two filters, as light from a wide angle that would make it to your sensor normally are blocked by the filter ring of the second filter. This is called mechanical vignetting.
Note that if you are using a lens designed for a full frame camera on a cropped sensor body then it is unlikely to be an issue unless you are using a pretty wide angle lens. Also if you are using a zoom lens and are zoomed in this is very unlikely to affect you.
Other than that you might want to try some test shots with both filters attached and see how the corners of the image cope with the extra filter.
An additional issue is that some light will be lost with every filter. UV filters don't block much light, but they do a little. The polarizing filter will block some more. So in situations where it's borderline whether you can shoot handheld, removing the UV filter might make the difference.