1) Don't use movies for research. Every genre has it's cliches, and some are based on things frequently shown in movies. But, honestly, movies aren't very realistic.
2) Think things through. Also, imagine what a scene will look like and if the actions the characters are taking will really work.
3) Keep track of what you know versus what the characters know. For example, if the characters thought they were safe at the end of a scene, then it's odd when (because the author knows what's coming next) they're acting like they're not safe in the next scene. Or if they should be afraid but the author knows they won't be hurt so they act unafraid.
I'm not sure how this will go over, but...
[The scene wavers before you...Hero just saved Heroine from the bad guys in a suitably dashing, brave, and last-minute way.]
They raced to the nearest horse, sounds of pursuit behind them. Hero lifted Heroine up behind the saddle then vaulted onto the saddle in front of her...or at least tried to. His foot hit the horse's neck (much to it's annoyance) and his thigh hit the saddle horn. He fell face first over to the other side.
After recovering and acting like that had been his plan all along, he grabbed another horse. They rode off at a gallop. Luckily, the roads were straight and made of dirt for the horses might have slipped and fallen while making a sudden turn at that speed.
The next day, they halted their horses at a river. Cynical Reader waved at them from where she sat on a nearby boulder, but they ignored her as they dismounted.
Hero surveyed the situation. "If we swim to the other side, the hounds won't be able to follow our scent."
Cynical Reader piped up. "I thought you lost them in the rain yesterday."
Hero brightened. "Oh, yeah, right. Why are we pushing ourselves so hard, then?"
"On the other hand," Cynical Reader said, "The downpour was raining on you during your escape rather than after it. You left a bunch of muddy hoof-prints all the way to this river."
Hero frowned. "You mean the rain didn't wash our tracks away? I thought it would."
Cynical Reader pointed at the muddy trail behind them, but then relented. "Well, maybe some."
Heroine moved closer. "We followed a paved road part of the way, so we didn't leave tracks there."
Cynical Reader said, "And when they don't find tracks on the other side of that road, where do you think they'll look?"
"But they don't know which direction we went."
"They have lots of people after you. They can split up. Plus, the dogs can still track your scent since that was after the rain stopped."
Hero cut in. "If we release the horses and cross the river, they'll follow the horses, right?"
Cynical Reader shrugged. "Could be, but the horses won't go far. There's juicy grass right over there and you haven't let them eat in over a day."
"Ha! Easily fixed." Hero turned and smacked the butt of his horse. The tired horse cocked a back leg, looked back at Hero with its ears laid back, and considered whether it was worth kicking Hero or not.
"Nope. That only works in movies."
Just then, baying hounds followed by enemy warriors on horses burst from the forest into the unnatural clearing at the river's edge. Hero vaulted back into the saddle and charged his horse at the lead enemy. When they were close and Hero was set to swing his long sword/club/short-range weapon, both horses suddenly swerved away from each other.
"To fast," Cynical Reader commented. "Horses are smart. They don't want to hurt themselves by hitting against each other. Even with training, they don't like getting too close at high speed."
Hero, thinking fast, used his long-range weapon--which was capable of breaking bones, knocking people out, and so on--to send a projectile into the hand of the next enemy. The enemy dropped his weapon, cursed, and drew his knife, which he threw at the Hero.
"Um," Cynical Reader said. "Why didn't Hero use his long-range weapon first to eliminate as many foes as possible before he had to fight them one-on-one? And since he's a perfect shot--apparently even from horseback, though he's never practiced it there before--why didn't he use his long-range weapon to knock out his enemy? Not to mention, Heroine, you have a long-range weapon, you're good with it, and these guys want to do really bad things to you. Why aren't you shooting them?"
"Um." She said. "Because I'm admiring how brawny Hero is?"
And so the day went, with Hero and Heroine in more distress from Cynical Reader's constant remarks than from their pursuers.