Graeme,
It used to be that most transistor radios had 3 or 4 seperate bands.
The standard 1970s 3 band radio had FM/MWand SW.
FM= Frequency Modulated, MW=Medium Wave or AM band reception and SW=Short Wave or High Frequency reception.
The radios with a single SW Band tended to be limited in the band width but were able to pick up the ABC "Radio Australia" foreign transmissions among other things such as "Co-ordinated Universal Time Signals" (eg a recorded voice latched into the transmission would say "At the tone it will be 21 hundred hours, forty three minutes and thirty seconds. Blip, blip, blip, BLEEEP.")
These signals are very handy for anyone using a sextant, nautical almanac and chronometer for offshore navigation. Accuracy of recorded time of sightings is vital for this method of navigation.
The advent, accuracy and reliability of the Global Positioning System has fairly much put that method out of practise.
A problem with the older radios with a manual tuning dial was that the radio would tend to drift off the tuning and many were fitted with a fine tuner.
That type of radio has come back into popularity as have turntables for playing vinyl records. However the newer radios mostly have a digital tuner which allows you to tune into a specific frequency with accuracy and the tuner will hold the signal better.
In answer to your question; yes these receivers can be handy for receiving "scheduled" (skeds) weather information transmissions. For the radio receiver to be of any use to you for getting that information you do need to know the time of the skeds and the frequency on which they will be transmitted.
You can get that information from the Department of Transport and Communications or the Australian Maritime Safety Authority.
Aldi recently advertised such a radio recently for about $40 and as you say Tandy and Dick Smith have them also. For $40 to $140 they are a fairly handy thing to have aboard but only of use if you know HOW to use it.
If you are going to buy one I recommend getting one that is capable of being powered from an external DC power supply as well as internal batteries.
I hope this information helps you. Cheers Cisco.