Which one of the following is the correct one?
- I should have seen it glow.
- I should have seen it glowing.
Or are both correct? Would you parse them please?
I would say that they both can be correct.
"I should have seen it glow" implies that you should have taken notice at the time the item started to glow. (Effectively, "I should have seen it [when it started to] glow.")
"I should have seen it glowing" implies that the item was glowing for a significant length of time, and you never noticed it during that entire period. (Effectively, "I should have seen it [while it was] glowing.")
Since memory motel asked for this to be parsed:
In both cases, it is the direct object of see. The gerund-participle glowing is a complement of see as is the bare infinitive glow.
It may be interesting to look at the passive versions:
Notice that in the passive, the bare infinitive will not work, but the to infinitive will.
The verb make also follows the complementation pattern OBJ + BARE INFINITIVE (e.g., I made it glow) but not OBJ + GERUND-PARTICIPLE. In contrast, caught allows OBJ + GERUND-PARTICIPLE (e.g., I caught it glowing) but not OBJ + BARE INFINITIVE. Different verbs allow different complementation patterns.
Also, I agree with David Wallace that there is no difference in meaning.
OP's specific example contains some irrelevant elements. All that's under scrutiny is the possible significance of using the -ing (continuous), or the simple (bare infinitive) verb form. So first of all it's important to note that these are both non-finite (they have no tense, or "time" aspect"). This might be better illustrated by considering the possible alternatives...
...from which it should be clear that the tense of the main verb (to sing) makes no difference to the component we're looking at. It's equally irrelevant how we interpret OP's "should have seen" (which might have various implications).
Having got those points out of the way, I can say that in many contexts it makes no difference which non-finite verb form is used.
A pedantic defence lawyer might say "Your Honour! The witness is speculating!" on the grounds that just because the defendant was seen to be in the process of stealing that doesn't mean that he actually completed the action. But normal English usage isn't usually "put on trial" like that.
Thus in practice, it's usually a stylistic preference which non-finite verb form to use. On average, people use the simple "unmarked" infinitive unless they want to emphasise the continuous and/or the [potentially] non-completed aspect of the activity being referred to. But even where it's certain the reference is to a continuous activity that never completes, this needn't affect the choice...
I've never heard anyone use rotting there - but obviously they expect the activity to last forever!