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What does the "Deep Analysis" do?

"Deep Analysis" does two important things:

It verifies that the output file size will NOT exceed the standard 4.37Gb limitation you have with a standard single layer DVD-R.
It greatly improves the output quality of the backup. What it does is analyzes each individual scene of the DVD, and decides how to allocate the bitrate (compress some scenes more than others.) so that the overall output quality will be better since DVD Shrink can apply the compression more accurately. (By no means am I implying that if you do the "DA", you wont have those artifacts or pixelation! I do a "DA" on every one of my backups.)
When using the "DA" feature, your backups will take considerably longer than before if you weren't using "DA". (Usually around 35 min up to an hour depending on the amount of compression that is going to be used and the CPU in your computer.)

NOTE: If the "Deep Analysis" button or option is grayed out (meaning it won't let you select it). It means 1 of 2 things. Either "DA" has already been done for this particular DVD or there would be no compression is required

DVD Shrink 3.2 Quality Enhancement:

Adaptive Error Compensation or "AEC" as it is more commonly known is a quality enhancement feature released in DVD Shrink 3.2.

Although at high compression 30%+ (70% or less on slider) using AEC will provide better output results but better results come at a price - Time. The AEC settings love using up your CPU's juice. If you have a slow computer then it may take you a substantial while longer to make a backup, although (in my opinion) it is worth the wait. If you do not use the AEC settings your backup will be completed a lot sooner and you will yield similar results to version 3.1.7.6.

So which one to pick?

nwg gives this advice:

Using AEC under any setting is better than not using it. Max Sharp is the fastest, while Max smooth is the slowest.
I have found the default AEC setting is fine for most DVD's.
Max smoothness can be good when having around 50% compression. It can reduce or stop the pulsing/pumping effect that can appear from using too much compression.
The AEC is not normally activated at it full effect until below 80% on the compression slider. Max smoothness is activated all the time when it is chosen.
jellybean has suggested this rule-of-thumb guide for the AEC setting on various compression levels:

90-99.9% - Max Sharp
80-90% - Default Sharp
65-80% - Smooth
<65% - Max Smooth

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