'should be noteworthy' is correct and usable in written English.
You can use it to indicate that something is worth noticing or should be given importance. For example: "His courage and determination to achieve his goals should be noteworthy."
They should be noteworthy, even memorable.
Calacanis then asked him pointedly whether he had plans to work on his own startup in the future, and Graham gave a response that should be noteworthy for anyone thinking about taking the plunge into the world of entrepreneurship and technology startups.
The finding that the incidence of IAA, intraoperative bleeding and UTI after LA was higher compared with OA should be noteworthy, even though these were not statistically significant.
It should be noteworthy that RMI performs the lower NRMSE error than BPCA with the increase of missing rate r and decrease of complete ratio t (see the left figure of Figure 5, 6, 7, 8).
It should be noteworthy that the genes with nucleotide-binding site (NBS) and/or leucine-rich repeat (LRR) domains are known to be related only to disease resistance [ 30].
It should be noteworthy that mRNA upregulation of tumor suppressor gene PTEN warrants neither increased protein level for PTEN as increases in mRNA expression do not necessarily translate proportionally into protein expression nor PTEN in the wild-type as silencing of tumor suppressor genes through mutations is very common in cancers.
The interview has made headlines in the press mostly for the President's timetable on Iran, but it should perhaps be noteworthy for another reason: its un-noteworthiness.
It should not be noteworthy – we ought to have moved on from noticing gender in sport – but it is.
That position shouldn't be noteworthy.
That shouldn't be noteworthy at this point -- sadly, it still is.
Given the discrepancy between the upper-frequency hearing ability of mammals and all other vertebrates, it has been argued that in the study of vertebrate high-frequency audition, hearing above 10 kHz should be considered noteworthy [5].
