Google allows most businesses to verify their business listings with phone verification process.
When I verified my business, when Google Places was actually Google Local Business Center, they did not have the phone verification method. I used the old fashion postcard method in the mail that took a couple weeks.
But now, phone verification is fast, less expensive and easier for many.
However, there seems to be a bug preventing it from working for some.
Jay from the Google Places team posted a known issue report in the Google Places Help forum saying:
Some users are facing issues with phone verification. They get an invalid PIN error even after entering the correct PIN received over the phone. We're now working on resolving this issue and the issue should be resolved soon.
There is no ETA for a fix but someone did try it out over the weekend and it still was not working.
Forum discussion at Google Places Help.