Good questions.
To begin, the 1335 days are associated with the 3.5 years of Dan 12:7. These 3.5 years are the same as the 42 months of Revelation 13:5. The 1335 days are a part of the 1260 days and extend beyond them. Based on the precept set forth in Ezekiel 4:1-6 a prophetic day is a year of real time. And based on the fact 1260 days is 42 months on a 30 day per month scale, it can be seen an idealistic lunar calendar is used for prophesy.
Therefore, the 1335 days are representative of 1335 idealistic lunar years and when multiplied by 360 and divided by 365.25 you end up with 1315.811088 solar years.
It is my belief the abomination of desolation being placed in the temple of God is in reference to the true temple of God which was never a physical building, but mankind as Paul says. This is when the Pope ruled over the whole "world" unopposed. The Greek word world from Matthew 24:14 being oikoumene and meaning the extent of the Roman Empire. There were 3 Arian Christian nations taken out by Trinitarian Christian nations that encompassed the areas in which Rome once ruled. With their opposition out of the way the Catholic Church declared the only way to God was through them, and in doing that you had to go through the Pope. Therefore, when the Pope was established unopposed after the 3 different Christian nations were destroyed was the abomination placed in the temple.
The timeline starts with the inauguration of Pope Pelagius I on April 16th of 556 AD. To this is added the 1241.889117 solar years (1260 idealistic lunar years), which places the end of the reign of the beast from the sea on March 7th, 1798 and the end of the 1315.811088 solar years on approximately February 6th, 1872 (give a couple weeks both directions).
As far as anything special happening at that time, I think you could argue there would or wouldn't be something to mark it. Something I find interesting is that in 1872 the USA's economy overtook Britain's economy. It's also the year Charles Russell started up the International Bible Students Association. Although I will say that I am not a Jehovah's Witness, nor Seventh-Day Adventist for that manner. (I've never belonged to any denomination)
For the mark of the beast it needs to be realized the mark on the hand and forehead represent basically thoughts and actions, and that a lot of things can equal 666 when gematria is used. As far as two examples go, my ancestor said the Roman numerals in circulation at that time when added together equaled 666 and I also learned that the numerical equivalent of Christogram symbols (like the Chi Rho) can equal 666. Those who are not loyal to the beast will be exiled from common society, and I believe that over the course of the last 1000 years if you did not belong to Catholicism you were persecuted and hunted as a heretic.
As far as the rapture goes, I do not believe in one. If it is does happen it will be an allegorical representation of the internal rejuvenation of the Christian where they live in the world but are no longer of it.
Thoughts?