1) Lord or Mr, it makes little difference. Our information is out there whoever we are. For some it is more readily available, but nobody should think that a determined fraudster is not going to obtain a date of birth with relative ease. A birth certificate does cost money, but hey, there are expenses in every business. Also bear in mind the 1939 Register birthdates are not great when it comes to accuracy. If I was planning a fraud (which I'm not

) then I'd rather pay £9.25 to get the definitive birthdate instead of risking the cheap option and a couple of years at her majesty's pleasure.
However if news reports are correct, personal information about people can be obtained online for a matter of pence per item - that is where the business is, not trawling through the 1939 Register.
2) You say there is an "obvious error in processing of the 1939 Register", but is there? The response from the TNA says
The risk for the 1939 Register has been adjudged by the Government Actuary Department, based on the likelihood of someone living in 1939 continuing to be alive at age 100, to be 1.5%. Following discussion and agreement with the Information Commissioner’s Office regarding this dataset it was decided that this was a tolerable level of risk.
To me this reads that some very clever people from different organisations have sat down and looked at the problem and agreed that whilst there is a risk of living people's data being published, the level of risk is acceptable (given that any living person can request take-down as well).
The only way of absolutely ensuring that no living person's data is published is to simply not make any of the 1939 Register available until every person known to be born before the Register was taken has died. Is this your preferred option?
I'm actually more concerned that the specified level of accuracy in matching the death records means there are many records for people who have died that will remain closed with no apparent proposals to address this moving forward - until they hit the magic 100.
Ok, yes, it is possible to obtain an idea* of the date of birth without unlocking a record. But if you remember, there were certain adjustments made to the site in the early days because FindMyPast had detected unusual activity. I think it safe to assume that although FindMyPast may not be monitoring the site use to protect our privacy, there will be sufficient monitoring to detect large-scale 'probing' of the data. *But see the above comments about accuracy of this DoB
It comes back to the 'why' - why would a fraudster go to the trouble of developing a bot to obtain free of charge dates of birth of people who might, or might not, be living? Much less risk for a fraudster to identify a 'target' person, go online, pay £9.25 and get a nice accurate birth certificate.