if my mom claim me in her tax, but I am getting a job in another state and pay tax, will there be any problem?

Should not be any problems as long as you and your mother talk to each other about these matters and you CORRECTLY fill out and file your own 1040 income tax return after the end of the tax year during the 2013 tax filing season for this purpose.
W-4 Employee's Withholding Allowance Certificate

http://www.irs.gov/pub/irs-pdf/fw4.pdf?p…

Very simple and easy fill in the W-4 correctly and completely and just claim Single and -0- ZERO Allowances and then sign the completed W-4 form and give it to you employer at that time for the purpose of your federal income tax withholding amounts if any would be required to be withheld depending on the amount of your GROSS income for each pay period at that time.
And then if they should withhold any amount of $$ out for the FIT amount as an estimated advance payment of any possible income tax liability that you might have when you correctly complete your 1040 income tax return during the 2013 income tax filing season and you receive your W-2 form from your employer around the middle of January 2013 and if you have a $$ amount in the Box 2 for FIT you will get a credit for that $$ amount on your 1040 income tax return and might qualify to get some are all of the withheld amount back as a REFUND amount when you correctly complete your 1040 income tax return print a copy for your records and sign the copy to send to the correct IRS address for processing during the 2013 tax filing season.
W-4 Employee's Withholding Allowance Certificate

http://www.irs.gov/pub/irs-pdf/fw4.pdf?p…

Very simple and easy fill in the W-4 correctly and completely and just claim Single and -0- ZERO Allowances and then sign the completed W-4 form and give it to you employer at that time for the purpose of your federal income tax withholding amounts if any would be required to be withheld depending on the amount of your GROSS income for each pay period at that time.
And then if they should withhold any amount of $$ out for the FIT amount as an estimated advance payment of any possible income tax liability that you might have when you correctly complete your 1040 income tax return during the 2013 income tax filing season and you receive your W-2 form from your employer around the middle of January 2013 and if you have a $$ amount in the Box 2 for FIT you will get a credit for that $$ amount on your 1040 income tax return and might qualify to get some are all of the withheld amount back as a REFUND amount when you correctly complete your 1040 income tax return print a copy for your records and sign the copy to send to the correct IRS address for processing during the 2013 tax filing season.
Hope that you find the above enclosed information useful. 07/21/2012

As long as you still qualify as a dependent there is no problem. If you are over 19, not a student, earn more than 3800, and do not live with her then you are not a dependent anymore.

it depends on her eligibility to claim you as a dependent
defining a dependent is one who is not yet 19(or age 19 attending 5 months of full times school-finishing high school for instance) lives in the household of the parent 6 months and the parent provides more than 50 % of the child's support
if you do not fit these requirements you are then independent and claim your own personal exemption and standard deduction, if you are a dependent, only the standard deduction is available for you to claim on your tax return
and no there should be no problem, she files her tax return, you file yours on your income

It won't be a problem at all. You simply file as a "dependent" on your Federal and state's tax return.
If you live in one state, but work in another, you may have to file on a "Non Resident" form.

Your state's tax website can help. Also, some of those year-round tax offices have smart/bored people who are just waiting for someone to come in and ask questions. If you catch them outside their busy months (Feb, April, Sept, Oct) - they might even answer your questions for free.. or if you take them to lunch. :)

i highly doubt that there will be any problems, my mom still claims me and although we live in the same state, we do live 3 hours away and i have my own job, no trouble so far.