Is it possible to check the quality of a coax connection to a PL259
plug without taking the plug apart - i.e. simply by using a
multimeter?

Hi Andy,

With both ends in your lap:
shells, end to end - very low Ohms;
pins, end to end - very low Ohms;
shell to pin, either end - infinite Ohms.
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The above is an electrical contact/insulation (DC) check

To check the quality of the complete coax cable including the plug(s)
a 'coax loss' check especially when operating at the higher frequencies
is important.

Some antenna analysers (like the MFJ 259/269 ) have this coax loss
measuring facility. These instruments enable the user to change
frequency which shows the overall quality of coax + fitted plugs.

The best type of PL259 plug is the one with a cable entry arrangement as
in N-type plugs . This provides an excellent and simple braid connection
,without having to apply heat other than soldering the centre conductor
to the top of the pin .
These plugs are somewhat more expensive than traditional PL259 plugs
(equivalent US$ 6 in the UK) but imho it is worth the expenditure.

Frank GM0CSZ / KN6WH