These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Alternative Character Interpretation: The show could very well be one never-ending exercise of alternative character for Rosencrantz and Guildenstern. From a couple of not-that-bright and sycophantic extras that nobody can tell apart, we get two men who are inquisitive, intelligent (in different ways), passionate, and in way over their heads.
ROS (humbly): It must be your dominant personality. (Almost in tears.) Oh, what's going to become of us!
(And GUIL comforts him, all harshness gone.)
GUIL: Don't cry... it's all right... there... there, I'll see we're all right.
Ensemble Darkhorse: This story single-handedly turned Rosencrantz and Guildenstern into this for the original play. Many performances of the play now include the duo as major characters (whereas previously they often used to be cut for being yet another set of minor characters), and they're arguably more popular and well-known than all the other characters other than Hamlet himself.
As mentioned on the Main page, R&G is occasionally even run back-to-back with Hamlet by some theatrical companies, who use the same actors for the same characters in each play. And even when they are not running the plays together, Ros and Guil's appearances in Hamlet are sometimes staged to include injokes from the Stoppard play — such as having them enter flipping a coin, or Claudius accidentally calling them by each other's names and being corrected by Gertrude.
The film especially accentuates this trope, with Ros constantly tugging on Guil's arm, trying to get his attention, agreeing with everything he says, throwing his arms around him, etc.
Really, it's not surprising given the characters these two were based on.
Rosencrantz only begins to show interest in the Player's offer of "participation" after it's been revealed that the entire troupe of Tragedians are male. (Not to mention that his reaction in the bathhouse scene is ambiguous as to whether he's disturbed at having mistaken Alfred for a woman, or whether he knew all along and is simply embarrassed to have been caught looking.)