Back to a genuine response to the OP's question...
mholloway wrote:I've heard it's specifically something to do with automation of plug-in parameters, yes? If so, which ones?
It affects all automation in the project, including track and plugin automation, all parameters. The following is an excellent description...
understanding PDC problems and solutions
That's only half of the picture though. The other half is with timing based effects, such as tempo synced delays, filters, gates, etc. When those are inserted in a series after any plugin which introduces latency, the timing based parameters get out of sync with Live's clock by the latency offset, making the return audio from the effect itself out of time.
mholloway wrote:What is a typical scenario in which this problem arises (and thereby could explain why so many people are angry about it...)? I just feel like I ought to know...
This is a somewhat typical scenario for a trance project. Insert a synth which uses oversampling, followed by a reverb which uses oversampling, then insert the following series of effects: Tempo Synced Delay > Tempo Synced Modulation Filter > Tempo Synced Gate > Transient Designer > EQ > Sidechain Compressor.
In this scenario, the tempo synced delay will be processing the audio out of sync with Live's timing clock by the amount of latency introduced by the synth and reverb, and feeding the out of sync return into the tempo synced modulation filter, which has all of its modulations running out of sync with the timing clock, and then feeding the return into the tempo synced gate, with its steps also out of sync with the timing clock.
Next add automation to the Transient Designer, and you'll notice that the nodes on the visual grid are not aligned with the sound. So offset each of the nodes to compensate.
Now decide that the reverb isn't working, and replace the reverb with a different reverb which has either no latency or a different amount of latency, or delete it altogether, and notice that the automation on the Transient Designer is out of sync again, and needs to be moved one node at a time; plus the tempo based effects are processing the audio at a slightly different offset to the timing clock, and the track sounds different. It's not that bad, so we can live with it, so let's go ahead and move the automation nodes.
Finally, route the sidechain signal from a plain kick track to the compressor at the end of the chain. Notice how the audio from the sidechain is actually in sync with Live's timing clock rather than with the tempo based effects... okay, scrap that. Print the audio without the compressor and then run the audio through the sidechain. Cool. Add some track volume and pan automation.
Now start this process again with a new track, for a new sound, using a different synth and effects, with a different latency offset. Wait, the volume and pan automation on the track we just did are out of sync. And the tempo based effects on this new part are slightly out of sync with the previous one.
Anyway, that's a relatively straightforward scenario, which I hoped clarified the issue a bit, without any histrionics or sarcasm. I hope so, anyway.