Revealing mistake: When Bond stops to study the map at the beginning of the Amazon chase sequence, you can catch some brief glimpses of a black object floating in the water. This is actually the explosive charge used to simulate the initial mortar fire's impacts from his adversaries' boats. Keep a close eye on those 'shell impact' locations to spot them proper.
Factual error: When Bond and Goodhead's space shuttle enters space, it still has the main fuel tank attached. However, when Bond releases the fuel tank it falls downward. It should maintain its momentum in orbit around the Earth until atmospheric drag (which extends out to high orbit) causes the orbit to decay over many years.
Audio problem: When Bond is being shot at while motor-boating away from his pursuers in Venice, at one point during the chase, they shoot right next to a rope on his boat and a sound from a silenced handgun is heard when the bullet hits the wood. No one is using a silenced handgun.
Continuity mistake: When the bad guy is struggling with Bond at the beginning trying to get the parachute, just before Bond kicks the bad guy away for good, there are shots of Bond's face and he's wearing the kind of eye protection goggles Jaws has on, only in a clear color. Bond didn't have these with him and never put any on, and in shots after the bad guy gets the boot, he doesn't have the goggles on anymore.
Other mistake: Bond is pushed from the plane without a parachute, but can see he wearing a altimeter on his wrist.