Hermione and why she got the time turner: Special permission from the Ministry of Magic had to be sought to allow Hermione to use one, but her academic record ensured that permission was given.
Noticing movement is completely different to seeing someone. You notice a sound you don't see it.
Macnair: In the film adaptation of Harry Potter and the Prisoner of Azkaban, while the importance of not being seen while travelling back in time is stressed, Harry and Hermione pass by the Clock Tower Courtyard while following their past selves. However, the executioner was sitting there, sharpening his axe, so he must have seen two pairs of Harrys and Hermiones, though he was too busy sharpening his axe to notice them.
Power of the Time-TurnersTime-related magic is unstable, and serious breaches in the laws of time result in catastrophic events. Possible scenarios include a wizard or witch killing their past or future selves by mistake, or altering one's life path in such a drastic fashion that it can result in temporal anomalies such as un-births. As such, the Ministry of Magic seeks the strictest guarantees if it permits the use of Time-Turners: Time-Turner possession is hedged around with literally hundreds of laws, and the most stringent laws and penalties are in place to prevent their misuse. The longest period that can be travelled back in time without serious chance of harm to the traveller or time itself is around five hours.
The possibility of time travel within the Harry Potter universe may seem to allow many plot holes, but characters appear to use them for trivial tasks that have no effect on existence as a whole. The one notable use of a Time-Turner within canon, the Rescue of Sirius Black and Buckbeak, obeys the Novikov Self-Consistency Principle. This theory of time-travel, stating that "Nothing can be changed because anything a traveller does merely produces the circumstances they had noted before travelling," is incidentally reminiscent of J. K. Rowling's employment of self-fulfilling prophecy.
Catastrophic events that have occured have happened when people have gone over the 5 hour limit and actually saw themselves with their own eyes.