For more info, visit billiards.colostate.edu
Fouls in Pool and Billiards
... how to detect and avoid various types of fouls in pool.

(external web-link) for more information:
see Disc V of the Video Encyclopedia of Pool Shots
How can you tell if a shot is a double hit or not?

The following video explains and illustrates how to detect and avoid a double hit in various situations:
For more information, see NV B.2 - Mike Page's double hits, push shots, and frozen balls (YouTube) and "Rules - Part II: double hits" (Download) (BD, September, 2009). The HSV DVD (external web-link) also has a nice feature on this. Also, many example shots, with explanations for the appropriate rulings, are available here:
Clips HSV A.110-A.115 (external web-link) also show the effects of speed, cue stick elevation, and follow-through on double-hit avoidance for a chalk-width gap between the CB and OB. Unfortunately, clips A.110-A.112 and A.113-A.115 are from different viewpoints and were shot by different shooters with different amounts of follow-through, but the results are interesting nonetheless. Notice that the cue stick nudges the CB in mid air (i.e., the shot is a foul) in the 3rd (fast) stroke of A.112. This one is tough to call even with the high-speed camera.

The following videos show some interesting methods that can be used to avoid a double hit when there is only a small gap between the CB and OB: (YouTube Videos)
Here's some slow-motion footage of various fouette shots:
How can you tell if one ball is hit before another for a close-call legal hit?

See "Rules - Part IV: Which ball did you hit first?" (Download) (BD, November, 2009) and: (YouTube Videos)
Also, for many example calls along with explanations, see:
from Scott Lee AZB post: (external forum-link)

A great test of "split hits" is something Jerry Briesath showed me 30+ years ago...freeze three balls together, with the odd ball towards the middle of the side pocket. Place the CB directly opposite the three frozen balls. Try to pocket the single OB frozen to the frozen pair, trying to get a split hit. You MIGHT make it once in a 100 tries. Move the CB right or left of the balls a few inches and you can pocket the OB every time. This is a proposition shot from decades ago.
Is a miscue a foul if it results in multiple hits?

In the current rules (see WPA WSR 6.16c (external web-link)), a miscue is a foul only if it is intentional.

HSV 2.1 shows a good example of a typical miscue. HSV A.13-A.20 and A.98-A.109 (external web-link) show many more examples under different conditions. With most miscues, the tip slides along the cue ball, and the tip, ferrule, and/or shaft make secondary contact with the cue ball. The secondary contacts might partially explain the slapping sound you hear with a miscue. Normally, multiple hits on the cue ball results in a foul; but in case of a miscue, the multiple hits are not considered a foul under the current rules (unless the miscue is judged as "intentional"). For more information, see "Rules - Part V: miscellaneous fouls" (Download) (BD, December, 2009) and:
One case where a miscue should be called a foul is when secondary contact clearly affects the shot. Here's a good example where the miscue might not be "intentional," but it should be ruled as a foul, because secondary contact is obvious:
Another example where a miscue is a foul is with an intentional "scoop" jump shot.

Actually, an argument can be made that all miscues should be called as fouls. For one reason, miscues can create scuff marks and other surface damage on the CB (for an example, see: Is a Pool Ball Smoother Than the Earth?, (Download) (BD, June, 2013). Also, miscues with draw shots can easily damage the cloth. The following video of an elevated draw shot clearly illustrates why:
Also, the current rules require a single, non-prolonged, forward-stroke hit of the tip on the cue ball. All miscues involve the tip sliding along the cue ball (which can be considered "prolonged contact" and a non "single hit"), and most miscues involve secondary contact with the tip, ferrule, and/or shaft. Maybe all miscues should be called as fouls, because they are a result of either player error or intentional, unsportsmanlike play. However, the current "intention" of the rules is that only intentional and blatantly obvious "secondary contact" should be considered a foul. The shot in HSV B.28 (YouTube) is an example. Another example is where you miscue on a follow shot, and you trap the CB under the cue ... this embarrassing and unintentional miscue should also be called a foul, because there is obvious "secondary contact."
What is a push shot foul and what are some examples?

A push shot is where a shot in which the cue tip remains in contact with the cue ball longer than is appropriate for a normal stroke and legal shot. A push shot is a foul (i.e., it is not allowed). Examples can be found in the following videos: (YouTube Videos)

NV B.2 - Mike Page's double hits, push shots, and frozen balls 
HSV B.28 - frozen-ball kiss, miscue, and push shots and fouls
Mike Massey trick shot collection
Is a "scoop" jump shot a foul, even if there is no miscue or multiple hit?

Yes. Here is the pertinent quote from WPA Rule 8.18: (external web-link)

A scoop shot, in which the cue tip contacts the playing surface and the cue ball at the same time and this causes the cue ball to rise off the cloth, is treated like a miscue.

and, per WPA Rule 6.16c(external web-link), a miscue is a foul if it is intentional (e.g., if use to purposely jump the CB over an obstacle).

The following video shows and explains what happens with various types of illegal "scoop" jump shots:
Here's an example scoop shot resulting from an elevated draw shot miscue:
For many example rule calls along with explanations, see "Rules - Part I: introduction" (Download) (BD, August, 2009) and:
For more info, visit billiards.colostate.edu