I got a state income tax refund for tax year 2013 from the state of Maryland last year (2014). That refund is correctedly stated on the 1099G I received. However, subsequent to getting the refund, the state recomputed my tax and required me to pay more, which I did. Should that additional payment result in a corrected 1099G being generated? For example, if the original refund was $2500, and I had to pay $700 extra, should a new 1099G with a refund amount of $1800 be issued? If not, how do I enter the extra $700 payment on my federal tax forms (for year 2014)?
No, you deduct it in the year you paid. The 1099G is for the deduction you took a year before.
You add it to the State tax paid as you enter your Schedule A data.