As an American who works with some people who speak British English, the language differences are usually not a problem. Most words mean the same thing, and those that don't are usually concrete enough not to cause confusion (ex: lift, flat, chips). The tricky ones, though, are the ones that differ primarily in connotations. For example:

• In American English (AE), "quite" is an intensifier, while in British English (BE) it's a mild deintensifier. So "quite good" is "very good" in AE but "somewhat good" in BE. I think "rather" works similarly, though it's less common in AE and I don't have a great sense for it.

• "Scheme" has connotations of deviousness in AE, but is neutral in BE. Describing a plans or system as a "scheme" is common in BE and negative in AE.

• "Graft" implies corruption in AE but hard work in BE.

These can cause silent misunderstandings where two people have very different ideas about the other's view:

A: "I can't believe how much graft there was in the procurement process!"

B: "Yes, quite impressive. Rather keen on going above and beyond, aren't they?"

A: "And did you see the pension scheme they set up?"

B: "Sounds like they'll be quite well off when they'll leave office."

In this example A leaves thinking B approves of the corruption, while B doesn't realize there was any. It could be a long time, if ever, before they realize they misunderstood each other.

Are there other words people have run into that differ like this?