Given the minimal amount of time that the Reliant crew has to make an impression before events kick into high gear, I was impressed that the tedium of their mission and their exhaustion with it comes through so strongly. Chekov's log is already mentioned, but also the first shots of Terrell, to me, show a captain who'd rather be pretty much anywhere than where he is.
Apparently a line cut from the film would have made it explicit that CA6 was the 16th planet they'd investigated.
Yes, they made mistakes (and paid for them), but under the circumstances I can kind of understand how they'd become desperate to just find a planet that met the requirements and move on.
Again, I believe the novelization does include a couple of lines that note that what Reliant finds isn't exactly what they expected to find, but that the anomalous data is listed as being from an old probe (not sure whether that means an actual probe, or whether the Enterprise having been there before counts as a probe), and the crew don't give a crap because they're expecting to find a desert planet that might work for Genesis, and lo and behold they find a desert planet that might work for Genesis.