According to what people say about him, his merit [at swordfighting] is unrivaled.

beseech: beg.

Horatio has supported Hamlet throughout, but here receives his first concrete proof of the King’s villainy. He trusts Hamlet’s description of its contents and urges him to continue the story.

This allows Shakespeare, too, to keep his story moving without pausing over unnecessary details.

Often read as Hamlet’s yielding to the inevitable. See “but let it be” in Hamlet’s death speech below.

This could also be an implicit, ambiguous answer to the “To be or not to be” question. Hamlet never explicitly chooses death, but his return to Claudius’s court and decision to participate in the suspicious swordfight can be read (and played) as self-destructive acts.

https://youtu.be/EHUZ1_cxdyw?t=1m32s

This line may have helped inspire “Let be be finale of seem” from Wallace Stevens’s famous, and Hamlet-influenced, 20th-century poem “The Emperor of Ice-Cream.”

Told that the spectators are gathering, Hamlet answers in effect: “All in good time.” One last, brief delay before the inevitable?

Here as throughout the play, we’re on Hamlet’s schedule. See “the interim is mine” above.

The King has sent a messenger to ask Hamlet:

Why does this random Lord deliver the message instead of Osric? Perhaps Shakespeare is showing that Osric, who has just “run away,” is avoiding further mockery.

Osric is using a fancier term (“carriages”) for the sword-belt accessories called hangers. Hamlet mocks him by playing on “carriages” in the sense of gun carriages for artillery pieces, adding that the old name will do just fine.

More context on carriages/hangers here.

german: germane, relevant.

Artillery gun on disappearing carriage, 1896

Osric is trying to say that he knows that Hamlet knows that Laertes is good at swordfighting. To mock his rhetorical excess, Hamlet interrupts him and pretends to mistake his meaning at every turn.

Whether or not Osric understands he’s being mocked, he continues to flatter.

Riverside Shakespeare glosses (2nd ed., p. 1230):

differences: distinguishing characteristics, personal qualities.

soft: agreeable.

great showing: splendid appearance.

card or calendar: chart or register, i.e. compendious guide.

the continent…part: one who contains every quality.

Osric’s repetitive, overrefined speech resembles that of his fellow courtier Polonius. Shakespeare hints at the parallel by showing him praising Polonius’s son Laertes.

In fact Osric’s fawning, chattering style recalls elements of Polonius, Rosencrantz, and Guildenstern combined. His presence in this final scene may serve as a reminder of the three men Hamlet has killed: another possible reason for Hamlet’s hostility toward him.

Hamlet continues his mocking power play (see note above); Osric finally proves willing to contradict the Prince and keeps his hat off.

https://youtu.be/j3kkKldrYvU?t=1m37s