Lots of good suggestions so far, but here are a few more:
1) Tools>sketch tools> check sketch for feature. It will take you through problems in a sketch one by one (you have to fix the current one before it will show you the next one). You can also access this function by going to extrude and hitting the check box - it will launch your right in.
2) Get into contour select mode. If the sketch isn't valid, it will launch you into contour select when you go to the extrude dialog. By paying attention to the regions that highlight you can find the open contours really quickly (then use the select chain trick Jerry mentioned)
3) If you have a sketch with closed contours that are messed up because they contain multiple overlapping lines, the contour select tool doesn't care. I saw a good session at SWx world that used contour select to avoid fixing an imported sketches. Just select the contours to use and move on (disclaimer - I personally don't trust/feel warm to the contour select function, but it's there is you want to use it and I iamgine that many use it to great success)
Good luck
-Ed