There are a lot of Magic cards that are "weird" in some way- misprints, test prints, non-factory cut cards, oversized cards, etc. So how do judges determine whether they're legal for play in a tournament? Hopefully this article should help you understand how it works. It's largly a matter of judge opinion, so in order for this article to be most helpful, I kept it to facts about WOTC's general policy and common judge considerations- I left out any of my own opinions. Also please note that this only applies to sanctioned events- in casual play, you can do whatever your playgroup is comfortable with.
First of all, people often want to know what a card truly "is". That's a question for your local philosopher, not judges. What matters is how a certain person or group is going to treat it.
When it comes to tournament legality, there are two considerations- What card it's played as, and whether it's Marked. These are completely unrelated things, though they often get confused.
A card is Marked if it can be distinguished from the rest of the deck without looking at the front. A deck of only oversized cards wouldn't be Marked, but a deck with some oversized cards and some regular cards would be Marked. If you're playing with an unsleeved deck, any miscut would be Marked unless the whole deck is miscut in the same fashion. If you're playing in opaque sleeves inside toploaders, almost nothing would be would be marked. If, as most people do, you use opaque sleeves without toploaders, it comes down to what can be felt through the sleeve.
The main (but not only) cards that will likely cause issues with regards to Markedness are the following:
Double-sleeving cards can help alliviate some of these issues, and if you're really conmitted you can try playing in toploaders. If you're unsure if a card is Marked, sleeve it up and try to pick it out of the deck, or ask a friend to do so. The final arbiter is always the Head Judge of the tournament in question, so if you're still unsure, ask them before starting the tournament.
What card it's played as is a little more complicated.
A common misconception is that a card is playable as whatever the visible name says it is. This is false, and unfortunately this misconception really doesn't seem to want to go away. This Swamp/Plains would most likely be disallowed completely. Some judges might allow it as either a Plains or a Swamp, but you certainly can't assume that it's safe to play as either without asking.
The official guidance we have on this is from the Magic Tournament Rules, which say the following:
Players may use otherwise-legal non-English and/or misprinted cards provided they are not using them to create an advantage by using misleading text or pictures. The Head Judge is the final arbiter on what cards are acceptable for a tournament.
This is quite vague, and intentionally so. It's not feasible to comprehensively categorize the infinite number of types of misprints that could occur, especially given how rare it is for them to actually be played in tournaments, so WOTC allows the head judge to use their discretion. As such, you may receive different answers from different judges, so you should always ask the specific judge who's running your event.
In general judges are going to care about avoiding possible confusion or logistical delays. Cards with the name or text of one card and the art of another (such as the Wald Forest/Plains), cards with a large portion blanked out by a color error, cards with a second card printed over them, etc might confuse opponents, and so will often be disallowed by the head judge. Same for cards that are difficult to shuffle or difficult for the opponent to read.
The tournament rules also define an "Authorized Game Card" as the following:
Authorized Game Cards are cards that, unaltered, meet the following conditions:
However, these guidelines were not written with misprints in mind. Many judges will still allow square-cornered misprints or cards with a misprinted back. Once again, the way to know for sure is simply to ask them. Note that Wizards has made an official statement that non-factory cut cards meet the "genuine and published by Wizards of the Coast" criterion, so their legality will just depend on whether they meet the other criteria in the opinion of the head judge.
The rules for altered cards are a little more specific:
Artistic modifications are acceptable in sanctioned tournaments, provided that the modifications do not make the card art unrecognizable, contain substantial strategic advice, or contain offensive images. Artistic modifications also may not cover or change the mana cost or name of the card.
Some judges choose to apply the alter criteria to misprints, but most don't.
Lastly, the game rules include the following:
108.2a: Most Magic games use only traditional Magic cards, which measure approximately 2.5 inches (6.3 cm) by 3.5 inches (8.8 cm). Certain formats also use nontraditional Magic cards, oversized cards that may have different backs.
This probably rules out cards of different sizes, but again, it's up to judge opinion.
So what does all this mean? Well, it means if you're unsure whether your card is legal, ask the head judge. They have final say, and different judges will have different opinions. The answer is going to depend on how that particular judge interprets all of the points listed above. Don't forget to bring backup versions in case yours are disallowed. Some common considerations that judges may take into account are:
Here are some examples of how likely various cards are to be approved based on some informal polls I ran. These numbers are only general leanings of the judge community as a whole and are unlikely to reflect the opinions of any particular judge at any particular event. Also note that approval numbers on some cards may be skewed downwards due to the judges who didn't follow the instructions of "assume the deck is sleeved and none of the cards are marked".
NFC miscut onto a filler card
Factory miscut, probably a make-ready
Wasn't in the original poll, I'd estimate around 30% allow
NFC miscut cut by hand with pinking shears
Wasn't in the original poll, I'd estimate around 70% allow
Factory miscut at the edge of the sheet
Wasn't in the original poll, I'd estimate around 85% allow
32% allow as Misdirection
1% allow as Vernal Equinox
Sheet layout error, given the wrong text file
31% allow as Drudge Skeletons
2% allow as Swamp
Test print with a white back
Wasn't in the original poll, I'd estimate around 5% allow
A normal card on the front, the back is upside down
A normal card on the front, this is the back
Mini card produced by World's Smallest
Test print with the new frame and a lower mana cost
45% allow as Plains
9% allow as Malakir Soothsayer
Missing all yellow and magenta ink, and half the black on the border
Wasn't in the original poll, I'd estimate around 15% allow
Wasn't in the original poll, I'd estimate around 60% allow
Factory miscut and double-printed
16% allow as Snow-Covered Forest
2% allow as Snow-Covered Island
1% Notice that it's actually a regular Forest on the left and the poll options were wrong