Not only are we led to believe that Arnie (Season 1) and Miles (subsequent seasons) are different people, but Caroline says that it has only been a year since her mother died. So when Rose went away on a cruise with "Arnie" in Season 1, his wife would have still been alive (4 seasons of the show had passed) so Rose would have been the other woman at that point.
How is it that Miles' daughter can visit and talk about her late mother when in a later episode it's revealed that Miles is in the witness protection program, and is supposed to cut off contact with his family?
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In the scene in which the girls are sitting down to dinner at the table and Sophia is at the stove, Dorothy picks up and unfolds her napkin and places it on her lap twice.
Sophia: (walking in on Miles and Rose kissing in the kitchen) Oh, no, not in the kitchen! You'll dry out the cheese!
Sophia: Dorothy, do we know anybody named Cecelia?
Dorothy: Your cousin, Ma. She only has weeks to live.
Sophia: Oh. Next time I'll accept the charges.
Blanche: Oh, Caroline, one year after your spouse dying isn't anything. Why, I've had people call me when their wife was in intensive care!
One of the men: (referring to test driving the car) Blanche told me I'd be the first.
Sophia: She's been using that line for 40 years.
Rose: Okay who's ready for birthday cake?
Caroline: What's in it?
Rose: Oh it's a surprise and in some countries a vaccine.
(Dorothy is getting a date with a man Blanche is interested in)
Man: So i'll pick you up at 7:30?
Dorothy: Oh I feel so bad about this...make it 8:00.