Corrected entry: In "Horizon" they talk about going to visit a system to watch a geological event that will take place in a week from then. Mayweather says that this system is 30 lightyears away from them. By using the Warp speed calculator http://www.ussdragonstar.com/utilitycore/warpspeeds.asp you see that this trip would take about 51 days. Warp 5 is too slow to get there in time, but still they arrive in time.
Corrected entry: How in the heck someone like in Doctor Phlox's time frame knew anything about tribbles in the first place. It was 100 years before McCoy and Cerino Jones and 200 years before Worf and co. Guess Doctor Phlox can leave a note to Doctor McCoy about the tribble's life cycle and its predators.
Corrected entry: In the episode "Regeneration", how can the two borg that regenerate communicate, as you will know from the Voyager episode (Survival Instinct) for instance, drones that are severed from the collective (as these had been for 100 years) do not re-establish connections with each other. They only act as confused individuals. They can't have been in contact with the collective. If they were, it would not have been necessary for the drones to send the message to the collective at the end. We know that the original two drones were from the future, and therefore, if they were in contact with the present-day collective, the Borg would have tried to attack earth long before TNG.