What political leanings a news outlet has isn't what matters so much as their journalistic integrity- how often they get facts wrong, how much effort they make to avoid distortion of facts, and what they do when they realize they got one wrong. There are media outlets both on the right and the left that have very strong reputations for factual accuracy- the wall street journal, the ny times, the economist, the christian science monitor, the la times, the washington post, the journal of foreign affairs, etc. News outlets that have extensive and rigorous fact checking policies, they only get caught making a factual error very rarely, and when they do, they publish a retraction right on the front page and usually fire the person responsible even if it was just an innocent mistake. If you read a factual statement in any of those, the odds are about 99.99% that it is accurate. These are the sort of outlets that make only a couple factual errors a year. Some of them have very strong political leanings, but those opinions are supported with real facts.
Then there is another tier, that makes an effort to be accurate, has a fact checking policy, prints retractions, but for whatever reason hasn't managed to achieve that same level of journalistic excellence. CNN is in this category for example. They don't ever set out to distort things, when they end up distorting information or presenting something that is factually incorrect, they do retract it, but the pressure of filling 24 hours with news and the reliance on pundits makes that tough. MSNBC is probably at the very low end of this category, maybe tending towards the bottom tier. Generally speaking, most TV news is in this category, most second tier papers, lots of magazines. These outlets may make a factual error every month or so, but usually it doesn't seem to be intentional. Factual statements you pick up from a source like that which sounds a bit fishy you could verify for yourself.
Then there is the bottom tier- news outlets that do not issue retractions, have fact checking policies designed to give their news personalities a lot of "flexibility" with the truth, they clearly have an agenda and pushing that agenda or getting ratings is clearly a higher priority to them than a reputation for factual accuracy. Outlets in this tier typically get caught with a factual innaccuracy every day and the innaccuracy always serves the same agenda, they aren't random mistakes. Some outlets in this tier have a factual innaccuracy in virtually every story. This tier is where Fox News, Huffington Post, and WND live without a doubt. Every one of those organizations is caught presenting blatantly false information every single day and they never retract it. Information you hear in a source like this you should simply disregard out of hand. It is simply unreliable, it is consistently distorted, and central facts are completely omitted when inconvenient.
So, long story short, I would not say that the right wing media is more biased. That's not the problem. Nor would I even say the right wing media tends towards being less factually accurate. The problem is that the consumers of news on the right seem far more inclined to get their news from the least reliable options on their side of the fence. The best strategy for getting news is to read the top tier publications only, but read them from both sides, but if you really can't stomach news that has a different editorial lean, and you find the top tier ones boring, at the very least, stay away from the bottom tier... They did a study once comparing the comprehension of basic facts about the Iraq war for example where they found that Fox viewers were four times as likely to have false beliefs about factual matters in the war than NPR listeners, but that isn't the crazy part. The crazy part is that they were actually more likely to get the questions wrong than somebody who said they do not follow the news at all. Watching Fox actually made them less informed than just sitting around staring at the wall. That's why the bottom tier is so bad. It actively misinforms you.