Yes, the paper handles the vacuum issue very badly (Sections II and IV contradict each other, and Figure 22 says "(In 750mm Air)"). However, convective air flow is unlikely to be the cause of the anomalous thrust. I would expect convection to have a slow time constant as objects heat up and cool down, but the thrust turns on and off quickly in the paper.
I would like to see more plausible causes of the anomalous thrust. Any new physics discovery is extremely unlikely here, but so far the proposed explanations have been lacking.
Ionization of air might be one such possibility. The very high-Q cavity with tens of watts of input power may reach electric fields strong enough to ionize the air inside the cavity. The ions/electrons/air would need to escape the cavity somehow to produce thrust.
Vacuum compatible RF amplifiers with power ranges of up to 125 watts will allow testing at vacuum conditions which was not possible using our current RF amplifiers due to the presence of electrolytic capacitors.
This makes it sound as if these tests were not conducted in vacuum after all...
Karl's version of Parkinson's Law: Work expands to exceed the time alloted it.