In general what will holding an anti-hydrogen atom for more than a 1/10th of second allow scientists to discover? In general what will holding an anti-hydrogen atom for more than a 1/10th of second allow scientists to discover? 
Specifically, given that they can hold one for <1/10th of a second, what would they discover that have not previously been able to determine. Or if not known, what have they been able to discover to date?
 A: The ultimate goal is to be able to do precision spectroscopy of antihydrogen, to make sure that the energy states are the same as in ordinary matter. If there are differences between the energy levels of ordinary hydrogen and antihydrogen, that would violate "CP" symmetry, which says that if you change the sign of all the charges in some system, and invert the parity, every interaction should be the same.
We know that CP violation occurs in nature-- it's been observed in kaon decay, among other things-- and it's related to the observed asymmetry between matter and antimatter in the universe. The known sources of CP violation are not enough to explain the matter-antimatter imbalance in the universe, though, so there have to be other forms of it out there that have yet to be discovered.
From what we known about the interactions of matter and antimatter, any differences in the antihydrogen states would have to be very small, but laser spectroscopy can be used to do measurements of astonishing precision-- there are single-ion atomic clocks that are good to a few parts in $10^{18}$. Having the target atoms trapped for only a tenth of a second complicates matters, but a group at Argonne National Lab did spectroscopic measurements of the charge radius of unstable helium isotopes that don't last very much longer than that, so it's a good step toward the goal of doing spectroscopy.
Another thing that people talk about testing with anti-atoms is the behavior of gravity. Again, you need to have trapped neutral atoms for this, because electrostatic forces are thirty-some orders of magnitude stronger than gravity. That will also require extreme precision, and many more atoms than have been trapped to date, but the recent experiments are a good start, and the remaining issues are mostly technical, not fundamental.
