I bought a used 97 Mazda 323 BA 1.8L 16 Valve BP DOHC and the previous owner has no idea when the last time the fuel filter was changed ( he was pretty clueless about everything related to the car ).
There seems to be a bit of hesitation on acceleration and I was thinking of inspecting the fuel filter, but have no idea how to tell if it needs to be changed.
Even if the answer is, "you should probably change it just to be sure", I'd still like to know how to inspect it.
Just replace it.
You're talking about a car from 1997. If you don't know when the fuel filter was replaced, I'm inclined to believe that it hasn't ever been changed. Very quick Googling shows me that a 323 fuel filter from that timeframe costs less than $20 USD.
If you really wanted to assure yourself that it's a problematic filter, you could disconnect the outgoing fuel line, place a catch can under the filter, turn the key to the accessory notch and measure the fuel that comes shooting out into the catch can against a known amount that the fuel pump is rate to pump over that time frame.
I wouldn't bother because:
Even if it turns out that it doesn't solve this particular problem, you'll have at least one part on your car that you know the exact history of.
Remove it and take a peak inside. If it's full of sludge, replace it. If you're a cowboy, blow into it and see how hard it is to force air out the other side. If it's working, you should see some fuel vapors coming out. You could theoretically clean and reuse the filter if you blow in the opposite direction, ejecting the blockages. Should save you some beer money until you're ready to install a new filter.
Pro tip: (Only) In an emergency you can poke a hole in the filter with something pointy.
If you've done all that and the car still hesitates, it may be time to have the battery, ignition (distributor or coilpack, as the case may be), spark plugs and fuel injectors checked. Everything save for the injectors is pretty easy and usually free to check.
