What are mistakes beginners should avoid in Dominion?
The bottom line is victory points. Period. Nothing else matters. If something is not actively helping you get more or your opponents get less, don't do it. It seems obvious that I'm telling you to remember how to win, but its very easy to go super-heavy on kingdom cards until you realize its too late...
Most of the time, the way to get victory points is with $$$. When I was learning I loved to pull of the 10 card action combos that took me 14+ turns to build, but when I realized I still had only made 7$ by the end of it I started looking at things differently. Solution: Make sure you have enough powerful treasures and actions that give +coins. Gold is king!
Keep an eye on end-game. How many provinces are left? Which piles are low? What are your predictions for what people are about to buy? If you know you have the most victory points, sometimes you just want to make the game end as fast as possible. If you can use a Coppersmith to get 1 or 2 provinces early, and then use plenty of +buys cards to buy up 3 piles of cost 2 and 3 cards before your opponents decks really get rolling, go for it. Its so funny when your opponents have just built these gold stocked decks to nail provinces and they realize you just ended the game and won with 10 victory points.
Know what cards will maximize your average $ per card ratio. If you have plenty of treasures in your deck, a smithy is often even better than a gold. Likewise, if you have plenty of actions that give you +cards, make sure you have treasures to back them up. 
Know the difference between early game cards, mid-game cards, and late game cards.
Watch your terminal actions. There's nothing that sucks more than drawing 5 terminal actions and having to just pick one of them to play. Try to balance your terminals with you chain actions. On the other hand, don't overload on +actions if you have very few terminals. A few of my friends love the 'village idiot' strategy: get 6 or more villages and have giant chains of them every turn. If you're not using the extra action from a village, its completely and utterly useless as all it does is replace itself.
Know the basic strategies, like drawing lots of cards, big money, attack cards, and trashing your bad cards as early as possible. These are covered very thoroughly here, so I'll just leave it at that.
Know how to evaluate a kingdom set to see what strategies will be strongest. Note how each attack card will change things, and how you need to adjust your strategy. I cover this more in the linked post.