As a preemptive disclaimer, I've only seen the movie- I have not read the original source. However the movie made a few common fantasy mistakes, and here's what I think of them!
1) A farmboy whose only "training" consists of sparring matches with his cousin/brother grows over a very brief period of time to be a hero capable of defeating the corrupt king's second in command- a wizard known as a shade, who has made a pact with demons for his power.
The problem here is that this young boy (of 17) with no real training to speak of becomes (or IS!) very able to do things which he has no reasonable ability to do. Swinging a sword is very different from swinging a hoe- and a sword is far heavier. The musclemass he built as a farmboy would be nearly useless when attempting to hold a sword- forget the fact that in the middle ages most career soldiers began training with weapons as early as age 12 to accustom themselves to the weight, heft, and techniques of using them.
Secondly, when Eragon reaches the rebels, he immediately dons a suit of armor. Armor is not something I've ever worn, but a few of my friends in the SCA (Society for Creative Anachronism) assure me it's quite heavy- and I've held some, and it is. The endurance and pysical training required to wear a heavy suit of armor for long periods of time would have been beyond a boy of his training. As a farmhand, he probably had a pretty strong constitution, so simply wearing it for a while probably could have been fine- but to fight in it? Highly unlikely.
Finally, in the climactic battle, Eragon on his dragon faces the Shade on his flying dark-magic creature. Nevermind the fact that the physics of the battle are way off- the dark-magic beast carries the dragon by the neck, and yet neither creature falls from the sky- here we have the second-in-command to the King, and he is beaten by a farmboy. Purportedly his only weakness is to penetration of his heart. The only solution for Eragon, then, is to be thrown by his dragon's tail AT the flying Shade, land on his dark-magic beast, and stab him in the heart, in midair. Again, this wizard has shown the ability to teleport at will, levitate weapons on command, hurl bolts of arcane fire, and (finally) summon a dark-magic beast. Eragon has only managed to shoot an exploding arrow, which knocked him unconscious. It's simply implausible- but hey, maybe he rolled a few natural 20's on this one.
2) Magic is used as a deus-ex-machina.
Eragon and his grizzled-but-friendly mentor make a stop in a town which appears to be in the middle of the swamp. All of a sudden, the town is swarming with evil baddies! Eragon is in the midst of escaping across a bridge when a hand grabs his foot, tripping him up. He grabs for his bow-and-arrows and fires one off while muttering a phrase he'd never heard (intuition, the movie explains). The arrow glows blue and explodes on impact, destroying the bridge and the baddies on it. We're not talking a firecracker, here- this is more like industrial grade TNT. Later on, despite an earlier failure of Eragon's to perform the same spell on a human target, Eragon manages to heal his dragon of all wounds- a massive beast, mortally wounded from being bitten (and carried!) on the neck by a dark-magic beastie. It's a common problem in high-magic fantasy (see Robert Jordan) to use magic as a sort of instant fix. In a world where magic is an incredibly powerful tool that saves the hero's butt, it must concurrently be an incredibly powerful tool for saving the badguys' butts. Especially when the badguys are older and more experienced- and, shall we say, have made pacts with demons for that little extra oomph.
3) The rebels are ultimately good, the empire is ultimately bad.
Eragon runs into the rebels, and summons his dragon to him. Now is the perfect moment for the leader of the rebels to throw Eragon in chains and use him as a threat against the dragon, keeping it subdued- after all, a dragon dies when its rider dies. The leader of the rebels, an experienced dragonrider whose dragon was slain long ago, had the chance to once again ride on the back of a great winged beast, fighting (arguably better than Eragon EVER could) against the evil empire. Even if it wasn't the leader who took this action, did NONE of the former dragonriders among the rebels feel the temptation to steal the beast for his own use? Where did this pocket of incredibly pure-minded people come from, in a kingdom that spawned a vicious and oppressive empire?
4) The plucky rebels successfully defend against a massively larger invading force which is potentially also better trained.
When the empire's armies march on the rebel stronghold, the first wave is a wave of berserker-like units. Armed to the teeth but barely armored they burst through the rock wall (what??) and begin the assault. The rebels fend them off aided by the dragon- but wait! Here comes the imperial army, looking to be at least thrice the size of the berserker battalion- not to mention better armed, armored, and trained- with an elder wizard/shade leading them. And yet the rebels win? How were they not cut down by superior numbers while the dragon and its rider were distracted by the shade and his mount?
5) The king of the empire, a man who ruthlessly slaughtered his way to the top and then stayed there either by fear or cunning, has only one general- a shade whose incompetance is shown in nearly every scene of the movie. The king's solution? Order his shade to use MORE MEN!
The strategy of the ruling empire appears to be "First use this very small group of soldiers. When that fails, use the middle-sized group. If that STILL doesn't work, use the BIG group!" How did this man become king?? Wait- we know how. He instigated fighting amongst the dragonriders of the days past. Convincing some to join his side, he cut down his opposition, and then destroyed the dragons which had sided with him. Let's face it- these are not the actions of a weakling, or a loser- this man is possessed of a powerful charisma, capable of swaying his allies and then leading them with cunning efficiency. The years on the throne have taken their toll, however, as his only remaining strategy seems to be the one we've already examined.
Some solutions to these problems:
When building a fantasy world, make sure you apply the 'rules' of the world to everyone in it- good guys and bad guys alike. If magic is a deus ex machina and gets the good guys out of scrapes, then the good guys' fortunes should turn when they seem to be winning out over the forces of evil- after all, a well placed firestorm by the enemy warlocks would certainly turn the tables.
Always make sure that the leaders are in power for a reason. If they clawed their way to the top with cunning and ruthless efficiency, you can bet that in any realistic world they'll run their kingdom with the same charisma, the same force, and the same efficiency. These are experienced generals who have fought many battles- they've seen victories, and they've seen losses, so they know what to do. This goes not only for the king of the evil empire, but also for the lovable and kindhearted resistance. After all, lucky rolls aside, the superior tactics will win the day.
When there is only one of something in the entire world- no matter what it is- all humans are fallible, and will feel drawn to the power of controlling that item (or creature!). It would be more realistic to see someone like Eragon, in possession of the last remaining dragon, having to defend himself both from those who are clearly his enemies and simply want him dead as well as from those who would appear as his friends in order to gain control over what is his. This also produces something of a twist in the plot and can be quite an effective surprise- provided it's not overused. When a close friend turns out to be a traitor, it's cliche- when the group of freedom fighters we've JUST met does something cold and selfish to set back our hero out of their own desire for power, that's thrilling.
And finally, if your plucky heroes are going to be swinging swords and wearing heavy metal armor- make sure they've spent the time training to be used to the weight and use of such items. Even your non-humanoid characters- dragons who complain about having to carry three people should not all of a sudden be able to don heavy plate-metal armor over the whole length of their body.