I agree that it is important to correct your question in that you are seeing actual trades and not orders. Near the opening you are likely seeing the crossing of the opening Spins of NYSE and Nasdaq. You will see the same occur after the close with the closing NYSE Exchange spin.
During the day it is also possible that large prints are the flip out of an accumulation trade for an institutional account that is traded on a "net" basis. Net trading is where the market makers compensation is built into the transactions price rather than a commission. As an example consider that Institution X is has an order to buy 50,000 share market "Not Held" and will pay up 1 penny from the Market Makers average price. Market maker accumulates and trades as part of that order and the accumulation trades go to the tape (in smaller sizes) say 50 1000 share trades go to the tape at 10. Once full accumulation take place he flips 50K to the institution at cost + $.01 or 50k at 10.01. Since this trade is done at a different price from the average of the accumulation trades the trade reporting rules require the 50K trade to be reported.
Another possibility (which is similar) is with guaranteed VWAP transactions where a firm has an order and guarantees a client a VWAP execution for a block of stock. The trading desk will trade the order and try to make money by bettering the VWAP. At the end of the trade the client will be given a VWAP execution. If you see odd sub-penny pricing on these larger trades these are likely VWAP trades being flipped to institutions. Most times this trade go off after the close.
Note that many institutions trade on a fully disclosed commission basis where you would not see the flip of the large print, but there are some that still do trade net where compensation is built into the trade. This is mostly a matter of preference with one caveat (soft dollars can not be paid on net trading).
Erroneous trades are unlikely. The Large sized HFT print strategies described in the Adam Clark-Joseph "Exploratory Trading" Paper are probably more in the range of 1000-3000 shares and not likely the prints that the question is asking about. HFT strategies are very sensitive to risk and I would expect that this is not a common strategy. Not to mention that regulators have cautioned firm's against momentum ignition strategies such as this.