Many of these you may have figured out on your own or figured out as a result from reading the other tutorials. These are a few things that are immensely useful MSPaint that are non-obvious or don't have any UI directly associated with them.
If you resize the canvas with the stretch and skew menu, it will interpolate color values. That means if you have vertical columns that are a pixel wide alternating between black and white and you scale the width down by 50%, then the resultant image will be a gray. If you scale an entire canvas to something larger, say 200%, then it will make the resultant image somewhat fuzzy instead of pixely.
On the other hand, if you want your scaling to be a strict pixel sampling (grainy), then select a specific region with the selection tool before you scale up or down.
One common misconception of long-time mspaint users is that the Windows 95 and up version of MS Paint eliminated the color replacer tool from the Windows 3.1 PaintBrush. This isn't true. It's just hiding.
It's hiding inside the eraser tool. Select the eraser tool. Now select the color you want to replace as your foreground color (left-click on the color palette). Now select the color you want to change it to as the background color (right-click on the color palette). Now right click on the drawing area and everything that is the foreground color will turn into the background color.
The "Curvy" Tool
...is actually called a bezier curve. Most people I've talked to are convinced that this tool is completely and utterly uncontrollable. It's only a matter of practice until you are able to achieve high precision with the bezier tool.
The first point you click on is the start of the curve and the point you release on is the end of the curve. Now you must click and drag two more points. These are known as the "control points". You can probably find a rigorous mathematical definition of how the control points effect the appearance of the curve on Google. The point that you press the mouse down has no relevance. However, the point you mouse up on will be the first control point which will dictate the general direction of the curve close to the begin point. The second mouse-up will be the second control point which will dictate the general direction of the latter half of the curve close to the end point.
If you right-click while drawing, it'll undo that move. This goes for pretty much any tool. If you're using the pencil or paintbrush and decide you don't like the line, then you can right mouse click while you're drawing and it will erase that current move before it commits. If you're using the line tool and realize that you don't like the starting point, then right click before letting go of the drag will undo the line. Et cetera for all the similar click-drag-click tools.
However, if you are using the right mouse button as your first click for the tool (i.e. you are drawing with the background color) then the undo behavior goes to the left mouse button.
The Ctrl Key
If you want to duplicate a selection, then you can copy it and paste it. But if you are trying to do this as a form of "mass production" of a repeating image, then that gets somewhat tedious, especially since the pasted copy goes to the top left corner of the visible canvas.
Solution: rather than copying a selection, you can hold down the Ctrl key and click the image and drag it somewhere else. Rather than dragging the selected image, you drag a duplicate copy leaving the original in its spot.
Replacing an Entire Color
The color replacement tool does not have much range. If you want to change ALL of one color into another color, this can also be done quickly. First, use the eyedropper and right click on the color you want to replace. Select All (Ctrl + A). Cut (Ctrl + X). Now select the color you want to change the color to with the left mouse button and use the paint bucket to fill the entire image with that color. Turn Draw Opaque off (Image --> uncheck Draw Opaque). Now Paste. The color you wanted to change is now the transparent color of the image you pasted and the color you wanted to change it to now shines through.
Convert Grayscale to Line Art
Suppose you have a grayscale image that you want to turn into pure black and white line art. A scanned drawn image fits perfectly into this situation. You can save the image as a monocrhome bitmap. (File --> Save AS, select Monocrhome as the file type). One you save it, it will turn everything darker than medium gray to black and everything else to white. Now you can save the image back to a 24 bit bitmap and edit it as normal. This allows you to start drawing on top of scanned drawings and fully utilize tools such as the paint bucket and color replacement tool.
Similarly, if you want to turn a full color spectrum to a few simple colors, you can apply the same process, but use 16-color bitmap instead of monochrome.
Cropping an Image
Cropping a selected region is not directly implemented in MS Paint. However, pasting a large image into a small space will cause the bounds of the canvas to expand to accomodate the image. So to crop, select what you want to have cropped. Cut this. Now resize the image down to something really small. This can be done by dragging the little dot at the bottom right hand corner of the drawing area all the way to the top left, or by going into the image attributes and changing the width and height to 1 (I find the latter easier with hot keys: Ctrl + E, 1, tab, 1, enter). Now paste.
When you draw straight lines using the line tool on the thickest setting, they don't always line up the end points perfectly. This is an annoying bug. What you can do instead is use the 1-pixel-wide line and draw an outline of the thick line you want. Then use the paint bucket to fill it in. Not only does this give you cleaner looking lines, but you are no longer constrained to the 5 sizes MS Paint offers by default for line widths.
Polygon Tool is a Pain
If you want to create a straight edge with a large filled-in area on one side of it, naturally, you would want to use the polygon tool. A sample situation would be trying to crop out an object behind another object against a solid color background. Filled in areas with at least one straight line is extremely handy for this. Polygon tool requires you to click almost exactly in the same beginning point to complete the polygon. When you're zoomed out, this is nearly impossible to do with accuracy. A better way to get the same effect is to select the color you desire as the background color and use the free-form selection tool. Click at the beginning of the straight line surface and drag out the shape of the filled in area, and lift the mouse button at the other end of the straight line surface.
Shift Key Constrains Line Tool
If you hold down the shift key while using the line tool, it will force the line you draw to be aligned to the closest 45 degree angle. Often times you need to draw a line that's perfectly horizontal or perfectly vertical. Now it's easy to do so.
Ctrl + Plus and Ctrl + Minus
These will cause the current size setting on whichever drawing tool you currently have selected to go up or down. And it isn't just a shortcut key to choose a different size in the menu. This actually allows you to make the paintbrush/pencil/line/etc tool wider than the 8 pixel maximum shown in the menu. Note that this only works with the plus and minus keys on the Num Pad, not the hyphen and equals keys between the 0 key and backspace.