1992 Acura Integra Question: Shift Linkage issue?

It's possible there is an issue with linkage, but from you description, and the year of the vehicle, possibly more likely to be worn internal transmission components. How many miles are on the vehicle? Do you happen to know the service history of the vehicle, more specifically at what mileage the transmission has been serviced?
Typically if it was strictly a linkage issue, external of the transmission, it would affect gear engagement into every gear, the same way a very worn out clutch friction material would. When it tends to be 1 or 2, maybe even three specific gears, and they all engage a little differently, it would be more likely that those specific gears have worn synchronizer teeth. The synchronizers are what help the gear to engage, by helping to match the input shaft speed to the output shaft speed, if these teeth are worn they will easily cause the symptoms you are describing.
Your issues should be easily diagnosed by a well trained technician within a very reasonable amount of time. I say SHOULD be because I don't want to leave any of my fellow tech's hanging out to dry if this does turn out to be a one off crazy problem, but it seems to me to be fairly straight forward.
Let me know if you have any questions.