Is there any way to do a scan as of a particular date in the past? For example, could I do a scan looking for all the 20/50DSMA cross-overs on Jan 3, 2012?

Neither C2000 version 7 nor TC2000 version 12.2 have any built in backtesting features. In StockFinder, backtesting is provided using BackScanner.

It is possible to visually backtest the technical (but not fundamental) portions of a scan using TeleChart however. You could just use the current version of the formula as a Custom Percent True Indicator and scroll back to the appropriate date to see if there was a spike using Pointer Mode (select the period key (.) on your keyboard to bring up Pointer Mode, selecting it again twice will disable Pointer Mode):

Visually Backtesting Specific Symbols
Clipping your chart back to a previous date

It is also possible to write Personal Criteria Formulas based on past dates (again, this is only for technicals). You may wist to review the following section of the Online Help Files:

Days Ago parameter

There are two distinct ways to use historical data with Personal Criteria Formulas.

Any criteria can be used to scan X number of days back by adding '.XX' where XX is equal to the number of market days past to calculate for. An example of this is (AVGC21.21), which is a 21 day moving average 21 of close, 21 days ago. This use of historical data always refers to the market day XX number of days ago (in this case, 21). If you wish to use a specific date’s data, use the option detailed below.

The other method of using historical data is by specifying a precise date in history to use. For example, (AVGC21.'01/03/2012') will provide a 21 day moving average of close for January 3, 2012 (the period should be used in cases where the first method requires a period and not used when the first method does not use a period). Always confirm that the date you wish to use using this parameter was a market day.

So a Condition Formula for a 20-Period Simple Moving Average crossing up through the 50-Period Simple Moving Average on January 3, 2012 could be written as:

AVGC20.'01/03/2012' > AVGC50.'01/03/2012' AND AVGC20.'12/30/2011' <= AVGC50.'12/30/2011'

No similar syntax exists for the time of day in an intraday Time Frame however.