Many mistakes are caused by thinking about the wrong things
It's almost always better to avoid math and instead let the tools and materials hone perfect joinery. That usually involves nibbling up to things.
1/ Perfect half-lap joinery
Problem: Math is slow and introduces chances for error.
Solution: Let the saw dial in the depth by flipping a test piece repeatedly until the setting is perfect.
2/ Cleaner cuts on a table saw for long tapers
Problem: When ripping hardwood, a slow feed rate causes burns on the cut edge
Solution: Cut the piece about 1/16 inch too wide with the slow feed rate, and then run the workpiece through the saw slicing the last 1/16-inch off. This light pass at the end allows you to feed the stock much quicker, eliminating the burned edge.
They use a tapering sled/jig in the video example and insert 1/16-inch shims to set up the initial cut. After the cut is set up, they remove the shims so that the workpiece will be 1/16-inch too wide after the cut. Now, return the shims and cut the piece to size, sliding the wood through the saw quickly and with no burn marks.
3/ Dialing in Dadoes
Problem: It is challenging to cut tongues and tenons to fit dadoes and grooves.
Solution: Cutt the dado first. If you cannot cut the dado first, use painter's tape as a shim to slightly move the router bit, embiggening* the width of the dado or groove.
This concept can be applied to many situations where micro-adjustments are needed.
4/ Cutting perfectly-sized dadoes or grooves using a drill bit
Problem: Same as above, only different. If you use the stock that needs to fit the dado as a spacer against a stop block on a tablesaw sled, the dado will be exactly one saw kerf too wide.
Solution: Same as above, but also different. The workpiece must be offset from the stop block by a saw blade thickness to cut the second dado edge. A 1/8-inch drill bit makes an excellent spacer between the stop block and the workpiece in almost all cases.
Bonus tip: Use a saw blade with a flat tooth to end up with a flat dado.
* Yes, it is!