Does the term "offset" in Line 10 of Form 1040 apply to a multi-State situation where an underpayment to one State can be offset against a credit from a second State. For example, if a State tax credit is received in previous year for $3,000, but $2,500 is owed to another State is $500the correct amount to be included at Line 10?

No! If you owe one state some money, you must pay that amount yourself - you can't use a credit from one state to pay another.

Line 10 on form 1040 is where you report refunds of state or local income taxes that you received, which should hae been reported to you on forms 1099-G from the state(s). You report refunds as taxable income on your 2009 return only if you had deducted your state/local tax in the year you paid it. So for the example you gave: if you had deducted state income taxes for tax year 2008, and received a $3K income tax refund in 2009 on your 2008 sate income taxes, then you report $3K on line 10 of 2009 return. If you happen to owe $2,500 to another state, and pay that amount in 2010, you may be deductible it your 2010 tax return, using schedule A.