What does one do when the weather report has a bogus altimeter setting?
We might speculate why the METAR is giving innaccurate data, but the question asks, &quot;What should one do...&quot;
I will take the liberty of inferring the question to be &quot;what should one do if one is unable to obtain an altimeter setting for the airport from which he or she is preparing to depart?&quot; Note that this question could be asked due to an airport with a faulty weather reporting system (as in the question above), an airport without weather reporting at all (quite common, for example: D42 or S68), or an aircraft that is not radio equipped.
I will further take the liberty of answering from what I know: the FAA regulations.
I will point out that it is the pilot's responsibility to be familiar with all available information and this should include a thorough weather briefing whenever possible.
Under the FAA's jurisdiction, the relevant regulation is 14 CFR 91.121 (a) (1):

(a) Each person operating an aircraft shall maintain the cruising altitude or flight level of that aircraft, as the case may be, by reference to an altimeter that is set, when operating—
(1) Below 18,000 feet MSL, to—
(i) The current reported altimeter setting of a station along the route and within 100 nautical miles of the aircraft;
(ii) If there is no station within the area prescribed in paragraph (a)(1)(i) of this section, the current reported altimeter setting of an appropriate available station; or
(iii) In the case of an aircraft not equipped with a radio, the elevation of the departure airport or an appropriate altimeter setting available before departure

(Since all airports and terrain in the US are below 18,000 MSL, this applies to takeoff; the rules governing flight above 18,000—14 CFR 91.121 (a) (2)—do not apply to our question. &quot;Operate&quot; is defined in 14 CFR 1.1.)
We can go through this like a flowchart:
If &quot;the current reported altimeter setting of a station along the route and within 100 nautical miles of the aircraft&quot; is available, use that.
(Note that this could include current reported altimeter settings obtained by radio (ATC, flight service, or a nearby airport), phone call (briefer or AWOS), internet, or any other method that would procure the needed data.)
If no such station is available, then use &quot;the current reported altimeter setting of an appropriate available station.&quot;
Now, if the aircraft in question is not equipped with a radio, then (and I would read technically only then) the pilot is permitted to set the altimeter to &quot;the elevation of the departure airport or an appropriate altimeter setting available before departure.&quot;
Now, that being said, if a pilot is in the middle of the Idaho backcountry at Wilson Bar (C48), or on the face of an Alaskan glacier, with no cell reception and no real way to acquire a current reported altimeter setting despite being in a radio equipped aircraft, then actual practice will be to set the altimeter to field elevation and get on with it. However, the requirement to use a current reported altimeter setting remains, and should be acquired at the first available opportunity.