Lay/ Lie, Dove/Dived-Bad grammar or regional variation?

Somone with a better grasp of grammar, can you help me out with this please?

In the UK the past tense of the verb “to dive” is “dived”.
eg “He dived into the pool to rescue the drowning man.”

My understanding is that in the US the past tense is “dove”.
eg “He dove into the pool to rescue the drowning man.”

Hopefully I got that right…unless that’s just a common grammatical error?

So, my question is, in the USA is it considered correct grammar to use “lay” in the following sentences?

“He was laying on the bed”
“I’ll lay down.”

Personally I would say:
“He was lying on the bed.”
“I’ll lie down.”

The former way sounds “wrong” to me, although it seems a common turn of phrase amongst the Americans I know.

Is it bad grammar on their part, or just a case of two countries separated by a common language?

dictionary.com has an explanation of this.

No, it is not considered correct, but few people know the difference. Personally it drives me nutty. At least we Americans didn’t start the practice.

These are common in speech, but are generally recognized as poor grammar, especially in writing. What makes this more confusing is the past tense: “Yesterday, he lay on the bed.” That’s correct, but hard for people to remember. I’m kind of a grammar maven, and I have to think about which word is right.

Both dived and dove are acceptable in the U.S. — at least according to Merriam-Webster, which has this to say:

In my own experience in the central eastern U.S., I would agree with all the above, but add that I’ve never heard dove used as a past participle in speech either (“He has dove into the pool.”). Certainly not that I can remember; it just sounds way too wrong. I suppose somebody out there must be saying this though.

The proper usage and past tenses for lie and lay are exactly the same here as in the UK, I believe. Again, Merriam-Webster has entries on the words.

So, any American you catch saying “I was laying on the bed” you can feel free to smack, on my behalf.

Lie and lay are easy once you memorize them.

Lie, lay, lain.

Lay, lay, laid.

I lie down every day. I do lie down every day. I was lying down. Yesterday I lay down. Many times I have lain down for a nap.

I lay down the book. I do lay it down. I was laying down the book. Yesterday I lay down the book. Many times I have laid down the book.
Isn’t this fun???

Another “thing” to note is that “lie” is an intransitive verb; whereas, “lay” (as the present tense and not the past tense of “lie”) is a transitive verb. One lays down (or up) an object, but a subject merely lies (except when he’s telling the truth. :))

Wrong. The past of lay is laid.