Not a big mistake. Whether or not this fails to pass the completeness check is far from certain. As others suggest, checking "yes-filed" should be sufficient. It definitely will be sufficient (assuming this is what is checked for at least three of the relevant tax years) to meet the requirements.
Place of Birth:
Verification of identity has always been a huge, huge focus. Obviously place of birth is relevant. The fact the applicant is not required to declare this information does indeed invite curiosity. The answer to why, however, is beyond our view. Given the new-form muddle, oversight could easily explain why. But, it may also be that IRCC has so many ways of verifying this aspect of a client's personal history, it has deliberately left this out. As-is the form is long and IRCC is well familiar with how these things work, the longer the form, the more items to be completed, the more qualified applicants will make incidental mistakes leading to an increased workload.
But ultimately the why does not matter to applicants. IRCC will know this information.
The importance of nicknames and aliases:
The form and help and instructions declare that this information is needed to verify identity. Me thinks IRCC is leveraging its language usage here. The usual, ordinary identity-verification issue is about positively identifying the applicant as the same person who is applying, and that is the same person who obtained PR status, all being the same individual as identified by current forms of identification and IRCC's client number. Sometimes this has required distinguishing the identity of other individuals, such as those with a similar name, especially if the DoB is the same, especially if there is other concurring information about the individuals. This can be important to verify precisely who the applicant is, and to verify that the applicant is NOT this or that other person, such as someone with a criminal record.
This has always been one of the most important elements in immigration procedures generally, and in the grant of citizenship particularly. For obvious reasons.
But this new form at the least hints that IRCC has increasing interest in connecting the applicant to other aspects of the applicant's life. That the need to verify identity goes beyond establishing precisely who the applicant is, but is now also about identifying other contexts or events or transactions in which the applicant has been involved, toward more positively verifying things like job and address history.
The other names used item was, of course, part of previous versions of the citizenship application form, going back to before the first version I examined (nearly a decade ago). Part of the PR application process as well.
The scope of its implications, however, appears to have expanded dramatically. One rather salient example is the extent to which IRCC appears to be doing open source research about some applicants, including looking for information about the applicant in social media and online services like LinkedIn. One Federal Court decision revealed that IRCC not only scrutinized LinkedIn account information based on the applicant's name, but also information based on other names used by the applicant, and also variations of those names, including some names the applicant denied ever using and denied that the respective LinkedIn information was in any way about her. IRCC and the Federal Court agreed the burden was on her to prove she was not that person (and that she failed to meet that burden). But a big part of her problem was that she had clearly not been entirely forthcoming and honest in what information she did provide IRCC (may have been CIC at the time), and there was some overlap of information (prior work history for same employer as the denied name claimed to work for, and the employer information indicated only one such person with a similar name had been employed there -- but it did not otherwise show the LinkedIn identity was necessarily the same person as the applicant).
The take-away from this is that IRCC may use the other name information to conduct research about the individual in a variety of sources.
For the vast majority of qualified applicants, this should not cause any alarm. Actually, for the applicant who has been forthcoming and honest, this could work to the applicant's benefit, since cursory searches should readily identify and verify the applicant's use of names (or not using other names) in other contexts and settings.
Example: Take an individual whose name at birth was "William Jefferson Clinkton:"
birth certificate: William Jefferson Clinkton
baptismal certificate: William J Clinkton
school records: William J. Clinkton
one drivers license: William Jefferson Clinkton
another drivers license: William J. Clinkton
nicknames (including variations of name): Bill Clinkton; Billy Clinkton; William Clinkton (no middle name or initial); Willie Clinkton; perhaps even Jeff Clinkton
one employer's records and employee identification badge: Bill Clinkton
another employer's records and employee identification badge: W. Clinkton
another employer's records and employee identification badge: William J. Clinkton
name used in tax returns: William J. Clinkton (usually) but on some occasions, perhaps for another country, also used William Clinkton and William Jefferson Clinkton
passports and travel documents: William J. Clinkton
telephone accounts (over time): William Clinkton; W. Clinkton; W. J. Clinkton; Bill Clinkton
Facebook account: Bill Clinkton
LinkedIn account: W. J. Clinkton
Twitter: W. Clinkton
Instagram: W. J. Clinton
You get the idea. And this is someone who has never had a legal or marital name change.
If in contrast William Jefferson Clinkton was always known as William Jefferson Clinkton and never used any other name or variation in any of the various contexts I list above, and thus only declares this one name to IRCC, if this individual is someone who IRCC decides to scrutinize in open sources and other government records, it is a safe bet that IRCC will screen for all the variations listed above even though the applicant has not listed them.
And when IRCC draws a blank for all those variations, that will corroborate the applicant's information. That's good.
If, in contrast, IRCC does not draw a blank, but instead finds the applicant has used or been referred to by other names, not so good. Although, not so bad either if the other names are merely a variation of the primary name used for official purposes and the other information associated with the applicant is consistent with the applicant's information in the application. But NOT good if IRCC finds other names and information which conflicts with what the applicant has reported (this typically tends to be career or employment information) . . . of course IRCC should and I believe will be careful about being sure to identify information that is very likely associated with the applicant. There is lots and lots of information one will find with similar name searching which will not be about the applicant, but those results are almost always easily distinguished from the individual being researched.
Most of the cases in which I have seen LinkedIn loom as a problem source of information, it is because IRCC identifies the LinkedIn information is probably about the client and, typically, it makes some reference to experience working abroad which was not disclosed in the application. Oops.
But for those who have used multiple versions of their name, and who have properly, as in completely and accurately provided IRCC with their work and address history, such collateral research should quickly and simply corroborate the applicant, in effect reinforcing the applicant's information and giving the total-stranger-bureaucrat assessing the application greater comfort about the veracity of the applicant's information.