>> I don't think you can say a fact checker is slanted one way or another by finding a few examples of a bias
Allsides does a systematic review. Those are a few examples from the review. You can read about their process for determining bias at https://www.allsides.com/media-bias/media-bias-rating-method.... One part of the process is an editorial review:
"The panel looks for common types of media bias such as slant, spin, sensationalism, and story choice. We review the outlet’s homepage, headlines, recent articles, photos, and other content dating as far back as six months using online archival tools like the Wayback Machine. Taking into account all perspectives, panelists individually assign a number, between -6.0 and +6.0, that they believe best represents the bias of the media outlet. These numerical ratings are then transcribed into a weighted average."
>> The tweet argued that Cuomo said that the vaccine being developed under Trump was bad, but the thing he actually said was that he thought the roll out plan would be bad.
The statement that Snopes fact checked was "Did Gov. Cuomo Say It Was 'Bad News' Pfizer Vaccine Progress Came Under Trump?".
Cuomo said "The good news is the Pfizer tests look good, and we’ll have have a vaccine shortly. The bad news is that it’s about two months before Joe Biden takes over, and that means this administration is going to be implementing a vaccine plan."
If someone is going to call the original statement "Mostly False", then yes, I would consider them to have a left bias. Cuomo is saying that it is good that we had vaccine progress, but bad that it happened before Biden was President. That sounds like an awful thing to say, and from my perspective, Snopes is covering for Cuomo who said something he would probably in retrospect like to have said in a different way.