With hyperdrives...the galaxy can get incredibly small.
The Jedi did see some of those red flags, but the crisis and their blindness caused by the Dark Side, clouded their senses, since the Jedi rely on the Force rather than common sense. "Blind we are", as Yoda says.
The Jedi also took an active role in the Clone Army as a means of keeping it close to them. I think their reasoning was that if their clones were to be used against the Republic or Jedi, the Jedi might be able to keep that from happening if they can teach the clone and drive their development. The Jedi were almost correct. Their treatment of the Clones generally was rather good and the clones respected many of the Jedi and would never have killed them without Order 66 being engrained into the clones. Prior to TCW making the biochips a thing, Order 66 was thought of in two ways. One: A preprogrammed hypnotic order than could not be disobeyed (similar to the biochips), or Two: A preset plan that the clones knew about and would carry out as they were designed to do. The later was used a lot prior to TCW, but that set up for a lot of clones to fictionally disobey orders due to their connection with their Jedi Generals. The biochip removes the chances of the clones disobeying orders (unless said chip was removed). The novel of Revenge of the Sith seems to have it as a mix of the two. Order 66 is something deeply embedded into the Clones, so that when Cody gets the order he regrets that it didn't come before he gave Kenobi back his lightsaber. But also it is so natural for the clones to just obey an order, they don't question it, they don't get angry, they show no sign of hostile intent against their Jedi Generals. They just open fire. This defeats the Jedi's danger senses, resulting in many of them being taken by surprise, when normally one shouldn't be able to take a Jedi by surprise.