From my understanding, one concern could be the low concentration of CO2 in the flue gas leaving the turbine. It will make the CO2 capture by amines expensive. About 40-50% of the flue gas needs to be recycled in order to solve this issue. The recycled flue gas will replace the secondary air used for cooling the turbine.
We usually use gas turbines in the oil field when we have high centralized loads, the main challenge we face is actually the relatively low efficiency of the turbines 30% when compared to the gas engines (49% for some series in Mitsubishi & 45% for jenbacher), until lately a company called Turboden introduced something commercially new called "organic rankin cycle" which utilize the exhaust heat.Hence, increase the overall efficiency to some limits.
So, Here are the challenges IMHO as a consumer:
1 - High fuel consumption and low efficiency
2 - restriction on size
3 - low R&D when compared to engines
4 - limitations on onsite maintenance
5 - higher emissions when compared to engines of the same capacity.
NOx emissions, Flexibility, Efficiency, Availability, Reliability are the top priorities.
The base load operation era belongs to the past as the gas turbine engines are required to work in conjunction with their renewable partners effectively. Note that there is a priority for renewables in electricty grids, and this means that gas turbines will spend most of their life time in part load, transient and stand by modes.
Nox, Efficiency increasing via TIT and CPD, avoiding unavoidable off-design degrating, Realable a fast dynamic models, accurate, robust and fast controller respond, hot section material improving, flexibility in load and frequency control, and so on... It is depenedent on your research line.