I found tinyCAD addon the most helpful solution for this problem. It can be downloaded here:
https://github.com/zeffii/Blender_CAD_utils
You can install several ways but the easiest is to download the zip linked in the readme and use the Install from File option in UserPreferences > Addons. Then you can enable it as usual.
To use it, just select intersecting edges, press W and select TinyCAD > TinyCAD XALL
