For separate consideration, here are the mentions of roses in Hamlet:
[3.1.153-154]; [3.2.287-290]; [3.4.40-46]; [4.5.156-162]. And then of course “Rosencranz”.
I took a stab here at comparing the rose and violet in the play, saying, a bit awkwardly, that the rose indicates the virtues of those in power (royalty, the beloved), while the violet indicates the virtues of those who are in a subordinate role (courtesans, the lover) and concluding with the unlikely but lively idea, not very well expressed, that the 3.2 rose mention evokes somewhat the idea of having a romantic love for one’s feet.
But what can be said of the rose here with certainty? –That it indicates something positive, maybe something perfect (true of all mentions except 3.2); that it is mentioned mainly in the third act (none in the first, second, or fifth, and just one in the fourth); that it is mentioned more frequently than any other plant in Hamlet yet absent from the two passages most dense with plant mentions [in 4.5 and 4.7]; and that it is mentioned only in the abstract (no actual rose appears in the play)… Anything else?
(By the way, the Olivier version of Hamlet is a bit of a dud insofar as thinking about the relevance of the rose in “Rosencranz” is concerned, as Rosencranz and Guildenstern have been written out of the script and make no appearance at all).