What to check on a 2018 used Triumph Speedmaster?

Mine is a 2021 model so its "euro-5" compliant. Any Speedmaster prior to this should be Euro 4 which seems to be a little less restrictive about such things as booster plugs (an excellent upgrade to help with lean fuelling) and general tinkering and modification (euro 5 ecus have anti-tampering software). I have read that the ecu will throw an engine management light if you change the front and rear sprocket ratios too much...!
I cant say that ive read of any common faults on the Speedmaster so usual used vehicle checks should be carried out.
Suspension isnt the greatest ive found but there are aftermarket options to consider if the stock setup isnt to your liking.

The newer the bike the fewer the 'teething' problems found with older units. Triumph upgrades their bikes as problems arise on any newly minted machines. When the Rocket 3 came out in 2004 a problem with the output bearing cropped up (installed backwards) that was fixed in later bikes, same with the headlight power routed through the ignition barrel desoldering all the connections in the barrel (fixed by 2010). It took them a few years to find all the weak spots and correct them in later versions. The Bobber is pretty robust since the Bonneville platform has been around since 2000.