As I say, it does depend on the encode, but I stand corrected – just double-checked and it seems like VLC no longer behaves like I said it did. 
What used to happen, if a chapter didn’t begin on a new sequence and an I-frame, or if you used the scroll bar to advance in the movie, when playback resumed, since VLC only had B-frames and P-frames to work with (the I-frames are basically a jpeg of the entire screen… the P- and B- frames are essentially only what’s changed from the last frame) it would draw the “changed” areas properly, but the “unchanged” areas would just be a matte gray… the screen would look funky until it got to the next I-frame, and then full pictures would again be shown. This is what I was calling “garbled”.
But, I just checked. I don’t know what update they changed that, but now it plays exactly like the WDTV does… it starts on the closest I-frame with a clear picture, and not exactly where you tell it to.
I can tell because some things I’ve added chaptering info to. If I pick a certain chapter, playback on the WDTV would usually be 2 or 3 seconds on either side of the actual chapter point. VLC used to start at the specified frame, but the screen would be garbled, as described above, until the next I-frame was encountered. Now VLC starts at the same 2-3 second-off point that the WDTV does. Since they changed this in VLC in one of the recent updates, the screen no longer ever gets mangled like I’d described.
Media Player Classic, on the other hand, still behaves poorly. It will start on the exact time code, and it doesn’t garble the screen, but it messes up playback for me another way. If I pick a chapter, or use the slider, then when playback resumes, there’s no picture at all, just audio, until the next sequence begins. 
It apparently knows it doesn’t have the full picture information, so instead of generating a garbled screen, it just generates nothing.
But, because playback begins on the nearest sequence beginning on the WDTV, as it is supposed to, many people with pirated movies run into the odd effect of playback being up to 10 minutes off where they expect it. Some of the pirated movies floating around have very long sequences. So, someone’s merrily watching it, and goes to FF or REW 30 seconds, and when they push play, it starts playing like 2 minutes or 5 minutes or 10 minutes before or after the point they started FF/REW from. Then they come here and complain that the WDTV won’t FF/REW properly, because when they go to FF 30 seconds ahead, playback resumes 5 minutes before the point they FF’d from.
Usually a DVD will have 15-frame sequences… so you have about a half second of “accuracy” when trying to random-access a playback point.
It seems as if the encodes that Handbrake makes for me has sequences that are about 5 seconds long (i.e. around 100 frames or so). My “accuracy” is usually within a second or two of the expected point.
Some internet downloads (and PVR encodes) have much longer sequences. Occasionally, a PVR encode is only one sequence, and can not be FF/REW at all… it can only be played straight through.
It shouldn’t affect slow-mo at all, on either VLC or the WDTV. When the file’s playing, if you pause and then start advancing frames, it already has the full picture, so it makes no difference whether the next frame it reads is an I-frame or a P-frame or a B-frame… it can always generate the next frame with no garbling.
But, as I said, the 10 second and 30 second jumps you originally asked about, would work reasonably well with DVD material, and alright with Handbrake encodes, but would be utterly useless for a good deal of pirated material, due to the sequence lengths – playback simply can’t start properly where you’d expect it to.
