Caveat: I have not played Rifts since 2000, and my knowledge of the system is certainly out of date.
I second Wik's comment about the setting.
The typical description of Rifts is "great setting, awful mechanics," but I was never overwhelmed with the setting. The basic concept, a sci-fi fantasy mashup where anything and everything can happen, is badass. But Siembieda's presentation leaves me cold. Humanoid villains are too often depicted as simple "psychopaths" or "sociopaths" with no underlying motivation or characterization. This is particularly true of the Coalition States. Despite some language that not all CS citizens are evil Nazi scum, Prosek and the other high ranking CS officers are uniformly described as mustache-twirling fascists bent on Eeeevil for its own sake.
Supernatural villains are too often depicted as simple soul devouring psychic vampires. With little to distinguish one from another. Every Rifts worldbook is the same: whatever the local mythology was has come true, except some big ball of tentacles that eats misery is really behind it all. Ho-hum.
There is a hell of a lot of stupid, stupid, stupid looking power armor in those books. There is also very little consideration given to the impact that power armor would have on rebuilding in the post-apocalypse. In other words, every damn enclave of more than about 100 people seems to have its own line of five or more unique power armor models available for its defense. Armor that can fly at close to the speed of sound and communicate via long range radio. There shouldn't be stretches of uncharted wilderness. There should be a half-dozen or so warring states that have carved up the country already.
Also, the mechanics are poor. Mega damage is an interesting idea when applied to Macross-style super robots and a terrible idea when applied to pistols and knives. Not only is the system unbalanced, Siembieda doesn't tell you it's unbalanced, and he doesn't give the GM any way to estimate how powerful a given RCC, OCC or NPC will be.
