Not too compelling for science as it is practiced. If we restricted ourselves only to evidence that was continuously witnessed first-hand, as it occured, we'd still be doing alchemy and astrology for a living. We wouldn't have QM, and we certainly wouldn't have galactic astronomy. It is a common enough thing for creationists to proffer the notion that inductive evidence is inadequate gruel to draw scientific conclusions from, because induction is fallible. However, science doesn't have the problem with it you'd like to make a case for, because a) science doesn't mind being fallible, and b) knowing it is fallible, science works very hard on being critical about the evidence it looks at.
Not at all. Galileo witnessed the revolution of the earth around the sun first-hand. Much of science is built upon first-hand observation. In fact, it really doesn't have anything else to go on. Science, by definition, entails first-hand human observation and reporting.