Based on the waveform posted in the other thread, it looks like that mix only needs the LFE inversion.
I don't have extensive enough data to say definitively, but it seems like the LFE delay issue primarily affected some (but not all) mixes done before about 2005. As
@DuncanS says, it's a byproduct of the filtering process - my feeling, again unsubstantiated by a ton of evidence, is that sometime around then the plugins or software used to create LFE channels were updated to automatically fix the offset created by the filtering process, ie if it induced at 6ms delay, it shifted the audio automatically by -6ms afterward.
I say this because since then (again, roughly, as I think there are some mixes from the 2nd half of the 00's that still have this issue) generally the problem has almost entirely disappeared - I don't think mastering engineers got wise en masse that it was something that needed fixing, I think advances in technology meant that the problem was no longer a problem at all.
So yeah, my approach generally is if it's a newer mix, I'll check for LFE inversion first, and if it's an old SACD or DVD-A mix, I'd probably look for the offset problem first. The offset one is a little more tricky as you're basically trying to eye-match the ridges in the main channels to the ridges in the LFE channel, so what I usually do is look for a passage that has a lot of bass energy (so I have a lot of visual information to work with) and then verify my results as best I can with a visual spectrum analyser and phase meter like Voxengo SPAN.