To the best of my knowledge the Molad is every 29.5 days + 793 Chalakim. Is there any information showing if the current Molad calculation is accurate scientifically? If it is off by how much is it off? How far off culmitavely are we now from the actual timing of the new moon?
I would recommend having a look at this site. The maths is much too complicated for me, but the upshot is that our molad is two hours later than the molad when the calendar was formulated, and is getting progressively later every year. The author includes a chart (and good luck to you if you can read it) that indicates the relationship between the actual lunar conjunction and the molad.
The same author (Dr Irv Bromberg) has written a number of online articles that concern the Hebrew calendar, some easier to understand than others. He has also advanced various proposals for calendrical reform, which he refers to as the rectified Hebrew calendar. It's definitely worth a look.
Just because the "error" in the molad moment seems small doesn't mean that it is insignificant. The approximately +2h delay relative to the mean lunar conjunction moment currently causes the provisional date of Rosh HaShanah (before the application of the postponement rules) to land on the "wrong" date (one day later) in 2/24 = 1/12 of years.
I am glad you asked this question, esp. just before Rosh Hashanna! I have been wondering about the same thing.
You may want to read this article.
In the present era the median length of the lunar cycle is about 29 days 12 hours and 30 minutes, the MSM is slightly more than 29 days 12 hours and 44 minutes, the shortest lunations are about 29 days 6 hours and 30 minutes, and the longest are about 29 days and 20 hours. Thus the length of the synodic month varies over a range spanning about 13 hours and 30 minutes! These variations were greater in the past and will diminish in the future:
The longest lunar cycles occur when Moon is moving slowest (near apogee) and Earth is moving fastest (near perihelion). The shortest lunar cycles occur when Moon is moving fastest (near perigee) and Earth is moving slowest (near aphelion). The declining mean Earth orbital eccentricity tends to reduce the range of lunar cycle variations. The average lunar cycle (mean synodic month) has miniscule long-term change compared to short-term periodic variations.
The article is quite technical, and I wasn't able to understand much of it. But, the summary, above, mentioning aphelion and perihelion, makes sense, if you understand the basic concept that gravity causes an object to accelerate as the gravitational force increases. Thus, when the moon is closest to the Earth, it will have a faster orbit.
There are other web sources that may explain this concept simpler. B"N, I will edit my answer after Yom Tov. Again, great question!
This article explains how far things have drifted over time:
To summarize it, there are two calendars in use (lunar and solar), and both are not quite 100% perfect. Of the two, the lunar calendar is a lot more accurate (it is off by about 1/7th of a "chelek", very reasonable to simply round it down), and the molad has moved "off" by only about three hours (backwards - the month is a little longer) since the calendar was first instituted 1650 years ago.