Warranty on replacements is 90 days from replacement or the remainder of the original warranty, whatever is longer.
One point to note for those sans AppleCare is that if Apple replaced a s0 with a s0, then it should - for the purposes of the two "part popping out" programs - assume that extra 2 year warranty from the original date of purchase for those defects. There are no such programs for the series 1, so the warranty will end at 90 days.
Upgrading as many people as possible to series 1s probably absolves them of a lot of responsibilities in that interim period. If the back or screen falls off my SS in the next 12 months I'm covered and will get it repaired for free. If the same happens to my wife's replacement series 1 after the next two months she's SOL despite us buying our original watches at the same time.