Some examples and common mistakes
I went through my pile of sketches to find examples of typical perspectives and also some things to criticize (it seems only fair that I would pick apart my own work). I didn't create bad drawings on purpose, of course, so there is not much method to this madness...
Greek vase perspective
To illustrate the usefulness of this non-perspective, here a series of sketches for what would be an entire comic page, all without any perspective. If I didn't foreshorten some arms, it could probably have been drawn by an Egyptian...
The one below is an almost perfect front and side plan view:
The drawing below shows a typical mistake of using inconsistent perspectives; the guncase is drawn in a 2-point perspective which places the all-seeing eye at a level just below the bottom of the drawing, but the characters are drawn as if viewed from their eye-level. Because of the guncase, it looks like the nearest character is standing in a hole, or the character in the back is standing on a soapbox...
The easiest way to avoid mistakes is to leave out non-essentials as much as possible. It also allows you to do neat tricks like this (OK so I'm probably the only one who thinks this is neat):
The size difference in the two characters below shows that this is a true perspective, yet the character on the right is drawn in undistorted profile. It would look better if she was redrawn with a little bit of perspective distortion.
Perspective isn't everything, of course. In the drawing below, the perspective couldn't possibly be more simple, yet the poor girl's proportions are all slightly off (and I didn't get around to dress her but that's another thing). I'm told every artist has bad days...
Japanese print perspective
The following is a cavalier perspective (I marked the axes with color):
Another cavalier perspective, the horizontal was given a slight angle to make it a little less obvious:
And below is an upside-down cavalier perspective. Really!
The following is an isometric perspective, though it's a bit hard to see:
There is no horizon in space! Fortunately two vanishing points always share one line... Something like below is not too hard to construct freehand. The hard part is when you need to draw it again from another angle. But I never actually went so far as to make a blueprint for guidance. I suppose now stuff like this can be rendered in 3D software if accuracy really matters...
In retrospect, the thing below should have been drawn in isometric. It wasn't, but who can tell the difference?
Three-point perspectives like this may look intimidating, but it's really not that hard. Here again, why didn't I draw this in isometric perspective? When you draw freehand, sometimes it's hardly more difficult to do the real thing.
Something like this on the other hand, with heavy perspective distortion to human anatomy, can be a real nightmare:
Keeping some distance, like in this tame 1-point perspective is much easier:
Or use photographs as reference, but that has its own set of problems...
You can also use a reference picture and paste in your characters, but then you must be able to match them to the existing perspective:
You can sometimes copy a complete setting, but unless it's for parody or homage, that's a really boring way to draw... (famous scene from “things to come”):
Now, on to the mistakes:
In the cockpit scene below, the blue and green lines are overlaid on lines that were supposed to converge to two points. Corrections in red. The bulkhead hatch should probably be centered behind the pilot, but it isn't. With determining lines after-the-fact like this, it is hard to be exact so you should not aim for absolute convergence, but big deviations should be corrected.
The next one isn't as bad except for the object in front, and the hatch is again not behind the pilot. The shape of the hatch is also bad...
The next drawing screams “perspective exercise”, but the lines don't converge, and the verticals aren't vertical. Use a ruler next time, don't try this freehand! Better yet, leave out all the meaningless details that have to be put in proper perspective but don't add anything to the drawing.
The previous were mostly problems where a few lines were off. A different type of mistake is when some parts of the drawing use a different perspective than other parts. For example, in the drawing below, the top part (green lines) has a different vanishing point than the bottom part (red lines). All that detail would have to be erased... At least this is an example that requires real perspective; a view like this is impossible in pseudo-perspective:
This one has a similar problem; the two characters on the left are in perspective with the eye level approximately at the heavy green line, the right part is a view from above with the eye level well above the top of the drawing. You usually get problems like this when you decide halfway to change the perspective of the drawing but you want to recycle some parts already drawn...
When you choose vanishing points to close to each other, you get a strangely distorted view like this:
Not leaving well enough alone is also frequently a cause of problems. In the little drawing before, the “tiles” on the floor don't go with the rest of the image. It would be better without them:
Similar to the problem above, the perspective of the three characters (green lines) is not too bad but the (unnecessary!) background doesn't go with it at all:
Totally random perspective like the one in the watercolor below; it's just bad... To be fair these were isolated character design sketches that I sort of connected together by putting some kind of room around them:
It's not always perspective that is the problem. In the drawing below, nothing is really wrong with the perspective, but something isn't right... The characters are supposed to be having a conversation, but the one on the left is talking to empty space! So stupid...
You can deliberately leave out perspective, and if you are blatant enough about it, the viewer will understand that you are using the idiom of symbolic representation. In the first picture below, the potted plant is totally unrealistic, it's almost the same as just writing "potted plant here" on that spot. Yet the viewer is not confused (at least I hope) because there is no information that contradicts the rest of the drawing. The second picture leaves the perspective to the imagination by omitting the bottom of the monitor, yet it has sufficient information to estimate the eye level!