Playing .MOV files are choppy on DVDs

Is there some magical procedure I need to do to get the videos to play smoothly?

You basically have two options:

1) As you yourself noted, you can copy the files from the DVD to your computer for QT playback or,

2) You can use an app like QT 7 Pro to re-compress the data and optimize it (user setting) for CD/DVD playback.

The problem with your workflow is the fact that the iPad videos are optimized for playback on a computer or mobile device. Such recordings may have data rates that very drastically during playback. Unfortunately, CDs and DVDs tend to read and forward data to the QT player at a more or less constant data rate. Thus, if the DVD player cannot provide data fast enough to the QT player, the media player must stop playback and wait until sufficient data can be cached to RAM before the player can continue its playback.

DVD players are normally rated in terms of mutiples of 300 Kbps. (I.e., a 12X DVD player can read/process up to 3.6 Mbps while a 24X unit can handle 7.2 Mbps). On the other hand, a current iPad 3 device can record/playback H.264/AAC files having instantaneous data rates anywhere from 0.1 Mbps to 14.0 Mbps for a Main Profile Level 3.1 file. While such excursions might not be typical in the same file, it is easy to see that the current iPad can easily record clips that have "average" playback data rates in excess of a DVD player's ability read/provide a constant data to the QT Player app. This is similar to internet streaming problems. Same cause and effect. I.e., if your internet connection speed is slower that the playback data rate of the streaming file, then the player may be forced to continuously stop playback while it caches additional data.

Now a technical question: How does changing the Data rate affect the quality of the video? I started with an 8x CD speed (2400 kbits/sec) but wonder if I should up it to a 12x or 16x. Since I am not sure what speed DVD-ROM the viewer will have I do not want to go too high and end up with choppy video again. But then again, any computer (Apple or PC) now-a-days should have a ROM drive 16x or higher, don’t you think?

Not sure if you are referring to the burn speed here or the encoded data rate of the file. Slower burns usually better in terms of the "burn" quality which may make a differece to some CD players. Encode data rates improve video quality up to a point but, of course, increase the size of the file you burn to optical disc. I normally use an 8X burn rate for maximum device compatibility and limit encode data rates to the 4.0 to 5.0 Mbps range. This is about the same data rate range used on single layer MPEG-2 DVD players and usually provides a "quality ceiling" greater than MPEG-2 DVDs since the H.264 codec is more efficient.

Also, is the Video Data rate and Optimized for CD/DVD-ROM the only things I need to change? I did not touch the Motion or Audio side leaving them at the default settings.

These two settings are the most critical since they determine how much data is packaged and how it is packaged. Frame rates, key frame rates, and other settings determing how data is distributed per unit of time but are more frequently used to improve the rendering of objects in motion or having complex motion vectors, better rendering of fades, change the "per pixel" data rates, etc. How you manipulate these settings is often a matter of personal preference depending on the actual content of the mendia and is frequently the reason why proper encoding is considered an "art" by some.