http://www.varchive.org/images/iv.jpg
He tried to explain this change via statements such as "The planets Saturn, Jupiter,
Venus and Mars, have moved upon different orbits within
human memory." and relating these changes to near miss encounters of the earth and other objects.

Pro: Biblical story of Joshua recounts a shower of large stones (Joshua 10:11) that occurred just before the day when the sun and moon stood still
Pro: A lot of junk consistent with the Biblical story above.
Pro: The following cultures used a calendar of 360 days for the year until the 7th century BC: Chinese, Chaldeans of the NeoBabylonian empire,  India, Persians, Egyptians, and Mayans. Most added five days to the calendar around the 7th century BC.
Pro: The circle, with 360 degrees may have been based on the "old" calendar.

Con: Between −708 July 17 and −686 March 23 there are about 265 months. During this interval, the accumulated error in the ephemeris of the moon cannot amount to more than about an hour, or 3600 seconds. Thus the length of the month cannot have changed by more than about 14 seconds in −686. Yet Velikovsky concludes that it changed by more than 6 days, from 36 days to 29½ days. The change that he claims is not consistent with any of the records before −686.
Big Con: Near misses between the Earth and other solar system objects would be observable in the current orbit of these objects.
Biggest Con: Common sense

There are no pro's. Velikovski was a psychologist not a physicist and came up with a large number of absurd ideas with no physical or astronomical basis. He hoped to explain human myths and religions.

Cons: The Earth's orbit and rotation are well understood and well documented by science. This is not some unsolved question or debatable point. The number of days in the Earth's year does not change rapidly and did not do so at that or any other date.

The following discourse by Dr. Carl Sagan illustrates just how
wrong
intelligent people (even with the prestige of a medical degree in
psychiatry) can be in their thinking, when they either have too few
supporting facts or find it too easy to ignore all of the facts as they
actually are.

Now, there is a curious argument alledging major recent
collisions in the solar system proposed by a psychiatrist named
Emmanuel Velocovski in 1950. He suggested that an object of planetary
mass, which he called a comet, was somehow produced in the Jupiter
system. He doesn't say exactly how it's produced, but maybe
it's.. spat out.. of Jupiter. Anyway, however it was made some 3500
years ago, he imagines, it made repeated close encounters with Mars,
with the Earth/moon system, having as entertaining Biblical
consequences the parting of the Red Sea so that Moses and the
Isrealites could safely avoid the host of Pharoah and the stopping of
the Earth's rotation at the moment that Joshua commanded the Sun to
stand still in Gideon. He also imagined that there was extensive
flooding and volcanoes all over the Earth at that time. Well, then
after a very complicated game of interplanetary billiards is completed,
Velicovski proposed that this comet entered into a stable, almost
perfectly circular orbit, becoming the planet Venus, which he claimed
never existed until then. Now, these ideas are almost certainly wrong.
In any scale model of the solar system like this, it's impossible to
have both the sizes of the planets and the sizes of their orbits to the
same scale, because then the planets would be too small to see. If the
planets were really to scale in such a model, as grains of dust, it
would then be entirely clear that a coment entering the inner solar
system would have a negligible chance of colliding with a planet in
only a few thousand years. Moreover, Venus is a rocky and
metallic hydrogen poor world, whereas Jupiter, the place that
Velicovski imagines it comes from, is made of almost nothing but
hydrogen. There's no energy source in Jupiter to eject planets or
comets.