He made the first telescopic observations
False. Thomas Harriot made telescopic observations at least four months before Galileo.
Sure, someone else looked through a telescope and drew pictures a few months before Galileo. Of course, Galileo independently came upon the idea, made a whole range of important telescopic observations (the phases of Venus, the moons of Jupiter), drew scientific conclusions from his observations and actually published his findings. That's why, even if someone else beat him to the punch slightly, Galileo's the one who's remembered for his observations, and I find rightly so.
He also conducted experiments into falling bodies on Earth, formulating a rudimentary version of the law of inertia
Which as an improvement on the pre-existing theory of impetus.
The pre-existing theory of impetus was dead wrong. This wasn't an update of a pre-existing scientific theory. It was a replacement of an old philosophical principle by a correct physical principle, in light of carefully gathered empirical evidence and the new understanding that the entire Earth is in motion.
Moreover, the idea that local bodies would influence their neighbors. Oresme for example raised this possibility 3 centuries before Galileo.
There were many individual aspects of modern physics which were anticipated by pre-modern philosophers. The ancient atomists correctly guessed, for example, that different forms of matter arise from different arrangements of fundamental building blocks. There's a very big difference, however, between positing an idea on the one hand, and deriving it from empirical observations and putting it into a coherent physical theory on the other.
Before the 17th Century, there were plenty of thinkers, and even experimenters, who came up with individual ideas that were approximately correct. But it wasn't until the mid-17th Century that anything resembling what we would call a scientific theory of physics was developed. The impetus for that development was given by Galileo's and Kepler's work, and the first correct principles of that physical theory were formulated by Galileo.
The basic laws of mechanics were unknown before the 17th Century, and the Aristotelian physics people believed in was completely wrong on the most basic physical principles.
This is a common misconception.
I think exactly the opposite is true. There are many people who study history of science, but who themselves have very little knowledge of science itself, and consequently mistake philosophy (or any form of experimentation) for physics. A symptom of this, for example, is calling Aristotle a physicist or calling the theory of impetus physics.