what custom of the Danes does Hamlet say gives them a poor reputation i other nations?

Answer 1

Heavy drinking and wild partying, and boasting of it while it in Hamlet's opinion should have been more honourable to breach with such undignified customs than to observe them.

Act 1, scene 4:

HAMLET

The king doth wake to-night and takes his rouse,
Keeps wassail, and the swaggering up-spring reels;
And, as he drains his draughts of Rhenish down,
The kettle-drum and trumpet thus bray out
The triumph of his pledge.

HORATIO

Is it a custom?

HAMLET

Ay, marry, is't:
But to my mind, though I am native here
And to the manner born, it is a custom
More honour'd in the breach than the observance.
This heavy-headed revel east and west
Makes us traduced and tax'd of other nations:
They clepe us drunkards, and with swinish phrase
Soil our addition;