Regarding the common complaint that nobody seems suspicious about the Republic being handed the clone army on a silver platter, has anyone experimented with beefing up the dialogue of the final Mace/Obi/Yoda scene in AOTC to suggest the Jedi do try to investigate between films, but had no choice but to accept the clones for the time being? Seems to me there are enough lines in the prequels about plots and puzzles to cobble something together. As a rough proof of concept based on nothing more than lines I remember offhand:

MACE: Where is your apprentice?
OBI-WAN: On his way to Naboo, escorting Senator Amidala home…Do you believe what Count Dooku said about Sidious controlling the Senate? It doesn’t feel right.
YODA: Joined the dark side Dooku has. Lies, deceit, creating mistrust are his ways now.
MACE: Nevertheless, I feel we should keep a closer eye on the clones.
YODA: I agree. Dangerous and disturbing this puzzle is.
MACE: Whoever placed that order did not have the authorization of the Jedi Council.
YODA: Speculation is all we have. Proof we need.
OBI-WAN: There is a massive shift in the Force; we all feel it. But I have to admit that without the clones, it would not have been a victory.
YODA: Victory? Victory, you say? Master Obi-Wan, not victory. The shroud of the dark side has fallen. Begun the Clone War has.

Granted, you would still have the potential issue that when ROTS picks up, it’s three years later and the Jedi are still working with the clones with no follow-up about that investigation, but then again they’re obviously suspicious enough that they want Anakin to spy on Palpatine.