My machine has brown spots of grease/oil appearing on the floor beneath it. The machine is still functioning but it is much louder than it used to be when filling and spinning. The model number is GW709AU.

I don't have this machine, but mechanical items with moving parts need to be oiled. I would check in your users manual. It should give you a schematic on the places to oil. Use sewing machine oil so it doesn't get all gummy and cause more problems.

If it is a mechanical machine, it has probably seized due to lack of regular oiling and cleaning. Mechanical machines require regular maintenance, just like your car. If your car is not greased and the oil changed regularly, it will cease working. Same with your sewing machine.

Take it to a repair service. In the future, be sure to clean and oil regularly (at least every 6 months if in storage, every 40 hours of sewing time) and use a fresh good quality sewing machine oil (not 3-in-1, WD-40, cooking oil, or the old brown stinky stuff in grandma's sewing basket). Apply only 1-2 drops of oil each spot as instructed in the owner's manual.

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because the function of filter is to block the small particles or dirty things including grease or oil etc., before disposing the water, and to avoid the clogging of floor drain and even sewage line. And after you used it you should check the filter if theres a some dirt, and grease or oil to clean up to avoid clogging and unclean water from your washing machine

The rear seal and the rear waher drum bearing is defective, this allows grease to get into the washer and that is what is getting on the clothes

There is a bearing seal that does tend to leak. Feel free to ask any other questions. I do recommend copy and pasting this link in your internet address bar under a new tab for more great repair info:

http://home.howstuffworks.com/how-to-repair-a-washing-machine3.htm

this sounds very much like that the bearings have badly worn-out,pain to replace them ?

Brown spots indicates a bearing is breaking up, the spots are the grease from the bearing and as the seal breaks down due to the bearings going off centre, the grease gets in the drum.
Get the bearings replaced if affordable.

If you have a front loading washing machine the oil is really the grease for the bearings that support the drum. The grease seal needs to be replaced, and if you are replacing the seal you might as well do the bearings. This is not a cheap repair because of the amount of labor involved in tearing the machine apart to replace the seal and bearings. If you don't repair the seal, eventually the grease will be washed out of the bearings and the bearings will be destroyed. You can tell if you need new bearings because when the machine is on the fast spin cycle it will sound like a jet engine taking off.

if your washer has a slight rumble noise when on the spin then it is most likely that your bearings are on there way out,what it is is the bearings have grease in them and once the bearings start to go this grease starts to leak into the drum which is what the brown spots are it also leaks at the back around the bearing at the back of your outer drum and also leaks onto the floor this will need fixing by a domestic appliance engineer but it is sometimes cheaper to replace the washing machine

chances are if you have eliminated anything thats got in by accident that the drum bearings are about to go, the drum bearings are protected by a water seal, this has started to leak and is now washing the grease out of the bearings back into the wash, you may also find a small amount of water on the floor, if you also remove the back and look behind the large pulley you may also see brown water marks running from the center of the outer drum

the next step will be a very noisy spin, like a rumbling noise

DRUM BEARINGS sorry