The demand for mechanical engineer/patent attorneys is not as high as it is for patent attorneys with other technical backgrounds, such as computer or electrical engineering. Unfortunately, aside from the automobile and airplane designers, no one is really focusing on cutting edge mechanical ideas.
I, for one, earned a masters degree in mechanical engineering and at the time had no plans to pursue patent law. However, while attending law school, I learned more and more about the field, and realized that my background was a good fit. To be honest, it was difficult to get a job with a law firm right out of law school because my technical background wasn't that desirable, so I worked as a Patent Examiner at the U.S. Patent Office for a couple years, and then moved on to a firm from there.
The mechanical engineering field is pretty broad, and includes semiconductor device processing and design and nanotechnology, which are both pretty hot right now. That's where I found my niche, anyway. But, even though you may be fully capable of working in these fields with a mechanical engineering degree, keep in mind that most law firms won't look at you for the simple fact that you have a mechanical engineering degree, and not an electrical engineering degree. I suppose they want to impress potential clients by showing how many attorneys they have on staff with electrical/computer engineering degrees.
So, my advice to you if you want to pursue patent law is to get another type of engineering degree besides mechanical (and definitely stay away from civil engineering). I think even materials engineering might be better, even though that is sort of a sub-major of mechanical engineering.
As far as other fields of law, perhaps you can try construction law, which requires some technical know-how. I don't know too much about it, but a friend of mine recently made the switch from patent law to construction law with no problem, and he seems to be really enjoying it (much more than patent law, I'm afraid).
I'm sure someone with a bit more experience can give you more info, but I hope this helps. Good luck!!