Bottom-line: there is only one for-sure accurate and complete source of information regarding travel dates, the one-and-only individual who necessarily was there every time: the PR himself or herself.
Not sure why CIC (now IRCC) has not routinely advised PRs the importance of keeping track of, and records related to, traveling abroad. The importance of this can loom very large for many, definitely so for those who travel frequently and are likely to have difficulty reconstructing the precise date for each and every trip if they have not kept the equivalent of a travel log.
The CBSA records have long been highly accurate, but as links18 notes, not necessarily complete. They are increasingly complete, but again the one most reliable source is the individual himself or herself.
Current presence calculator instructs applicants to give approximate dates and to explicitly note that they are approximate, if the applicant is not able to specifically give the precise dates. My sense is that this will work so long as all trips are disclosed and number of days absent are at least very close to accurate, but that omissions, extensive approximations, or significant discrepancies, will likely be more or less problematic.
As to whether failure to declare a trip that is omitted in the CBSA report might be noticed: foremost, the obligation, the requirement, is to declare ALL trips, and now this includes all day trips. While the primary source against which IRCC checks is typically the CBSA travel history, there are increasing reports that IRCC is conducting broad-based internet searches for information about individuals. Typically referred to as "open source" information, it is apparent that in some cases (not routinely, is my guess, but in some cases) IRCC is looking at Canada411, LinkedIn, Facebook, employer websites, among other sources of information on the Internet. There have been cases where such information refers to this or that event or activity or position abroad which is inconsistent with the applicant's declaration of dates abroad.
Note too, even inconsistencies between apparent activity IN Canada during time declared to be abroad, can result in damaging one's credibility. One might think that would, at worst, indicate the applicant might have made a mistake and was actually in Canada more than declared. But where this comes up in published decisions, it tends to actually hurt the applicant. (Older case I can recall was where the school records for an applicant's children indicated attendance at school in Canada during a time the applicant reported herself and the children to be abroad, and this was a negative factor relied upon to justify denying citizenship.)
Overall: best to not underestimate how critically important it is to accurately AND completely report all travel abroad, and thus to not rely on any particular source, including CBSA travel history, in populating the physical presence declaration. Rather, do one's best to be sure, as sure as possible (if one did not keep an exact travel log) based on multiple sources, to accurately and completely report all trips.
(Check credit card records, for example, and emails referencing dates in or out of Canada, any records one might have which would indicate trips abroad.)
Other than mistakes in completing the forms generally, probably the single most common cause of problems in citizenship application processing, and perhaps the most common cause of serious problems, has been the inaccurate or incomplete disclosure of travel abroad.
