I am building up a new system and the intel mother board I am using specs DDR3 1333 memory, is there a problem with using DDR3 1600?
If the motherboard supports 1600, then no problem.
If it does not support 1600 then it may cause the system to not power up, or at the minimum the bios will clock it back to 1333 speeds.
DDR3 1600 generally have a larger timings because of greater clock speed.
Timings are the numbers of clocks motherboard should wait during the memory fetch operations. And generally all memory modules on the same motherboard should be set up to the same timings. If you have already some DDR3 1333 modules and upgrade you motherboard with additional DDR3 1600 module you will probably have a slower memory system than before because it will operate on slower memory clock than 1600 and with larger memory timings than common 1333 modules.
Most motherboards allow you to play with this setup values and try to manually set smaller timings for 1600 memory modules. But, of course there is no guarantee of success.