Does a PhD give you global mobility in the job market? I am thinking of doing a PhD in Condensed Matter Physics at the Indian Institute of Science, which is not a bad place to graduate from as far as I've heard. 

The downside is I'll be a little on the older side by the time I graduate, and in India, there seems to be a starting faculty preference of 35 years. I would like to know if I'd be able to practice physics somewhere else in the world after getting a PhD in the area. 

I've heard the US is pretty open in terms of hiring foreign candidates, but Europe is not. What about other English speaking countries like Australia, New Zealand, Canada, etc? Does a Phd open up career opportunities world-wide?
There are two aspects to this question: the hiring process within an employer's institution, and the immigration policies which allow a foreign worker to move to another country and begin employment.

I think with respect to the first question—the hiring process and preferences of an individual employer—I think that in general, employers are looking for the best-qualified candidates, regardless of their origin. There are certain obvious exceptions to this (for instance, a foreign national will have a hard time getting a position at a National Nuclear Security Administration facility in the US), but otherwise, people will want the person best-suited for the job. I think this is true both in the US and Europe.

The other step is the national immigration policies. This is where things become more complex. For instance, if you are a non-European Union citizen, then your employer will need to certify that your experiences uniquely qualify you for this position, which can delay the hiring process somewhat. Similarly, employers in the US have to wait for you to obtain an appropriate visa, which can delay your start date significantly. This makes it sometimes less advantageous to hire foreign employees. (But this is a "speed bump," rather than an insurmountable obstacle.)