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Galley Proof are the preliminary versions of publications meant for review by authors.

Question: To what extend, one should improve the article in Galley Proof ?

Situations 1. If all the proofs are fine, just modifying few typo error, and misprint would serve the purpose. But

Situation 2. Assume all proofs are fine. ( No change in proof anywhere. ) You receive a reply from Journal after a year. By the time, you realize adding few remarks from same or some other paper and citing the other paper could explain Article to some good extent. Should one add such remark and cite the other paper.

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closed as off topic by Igor Rivin, Chris Godsil, quid, Bruce Westbury, Andy Putman Jun 6 '12 at 18:38

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One sometimes sees a note added in proof at the end of a paper –  Gerald Edgar Jun 6 '12 at 16:57
Not appropriate, voting to close. –  Igor Rivin Jun 6 '12 at 17:16
Ask someone at the journal. You'll get a definitive answer, which is not what you'll get here. –  Chris Godsil Jun 6 '12 at 17:55
The question is a bit unclear as the extent and relevance of the envisioned changes does not really become clear. Also in the title the question is 'can' and in the body 'should'. –  quid Jun 6 '12 at 18:07
Now that can/should is resolved, my opinion: one should make only very small changes or inevitable ones. Evidently errors need to be corrected and it can make sense to add new information that is really important (but see below). Also, if say slightly changing some sentence somewhere can eliminate a misunderstanding this is something that IMO makes sense. In any case changes should be very local or be put separately as Gerald Edgar points out. To add some remarks somewhere throughout the paper just because it makes it a bit better is IMO not appropriate. As Gerald Edgar mentions... –  quid Jun 6 '12 at 19:22