Going over this material again reminds me that we ought to think about encouraging learners of English to learn appropriate glottalization if they are aiming at copying a native-speaker model. Within the time that I can remember, its use has increased greatly; as long ago as 1952 Paul Christophersen wrote “If we are to continue to use RP as a model, has the time not come to take cognizance of the glottal stop not only in our scientific analysis of English speech but in our teaching? Or are we to teach an artificial pronunciation?”, and I think the need to consider the question is now much stronger.
If you have the CD-ROM or App version of CEPD, you can listen to some examples - the actors employed to make the recordings sometimes produced glottalization and sometimes not, though of course the script they were given didn't direct them one way or the other. In the word 'witness' you can hear that both the British and the American speakers have glottalization; However, neither has in 'hateful'. 'Blackboard' seems to have no glottalization from the English speaker, but does have it in the American. In 'butcher' and 'background' British has it but American not.
One way to increase people’s awareness of glottalization would be to show it in pronunciation dictionaries. It would be perfectly possible to include a superscript glottal stop sign (NB I don't seem to be able to do superscript with this editor) as an indication of where a glottal stop may be pronounced before a fortis plosive or /tʃ/ (though it is never obligatory). Thus the word ‘extra’ might be transcribed /eʔk.strə/ and ‘nature’ as /neɪʔ.tʃə/. Of course, this is not a true phonemic transcription, but similar non-phonemic information is already used in CEPD and LPD, the most conspicuous example being the use of the voicing diacritic to indicate “flapped /t/” in American pronunciations. For example, CEPD transcribes ‘latter’ as /læt̬.ɚ/ while LPD gives /læt̬.ər/. Yet the marking of flapping is redundant information, showing something that is predictable by rule.
What I am suggesting is just a personal fancy of my own, and not a policy decision for the next edition of the CEPD!
The distribution of glottalization is, unfortunately, not easy to explain, and we need to describe not only where we find a glottal stop preceding a fortis plosive or affricate, but also where we find complete glottal replacement (almost always of /t/). The Wikipedia material needs to be set out more fully and more clearly.