Use goo gone! It works wonders and is non toxic and totally safe to use inside the dryer. You can even use to to pre treat stained or greased clothing before washing it in the washing machine! Its just a natrual citrus extract. I use the goo gone gel spray, not the pro goo gone, just the regular! Spray it on a paper towel or old towel and just start to wipe it right away!

Or more precisely, condensation trapped between the wood and the finish. It usually dissipated over time (months) as the moisture is absorbed by the wood but there are things you can do for a quicker fix. The cloths mentioned work pretty well on light blushes. For a more aggressive fix on heavier clouding, you can place a chemise over the affected area and apply gentle heat using an iron. If you've never done it before, I would try some scrap piece first, but it's extremely effective, quick, and permanent. For the professional... using a chinese food carton with hot water in it will help produce some really good water marks to practice on. The wax in the paper (as it is heated) makes an excellent surface seal to help drive condensation under the finish. The mayo trick is just a short term fix... saturating the finish with oils so refractive light hides the blemish. As the oils dissipate, the blush becomes visible again.

The dark circle looks like a water stain.......and oxalic acid will remove that. And if you have other water black marks it will help with them too. Any mineral spirits should evaporate with time. I have had good luck removing grease stains on suede by rubbing with corn starch, then brushing it off....repeat and repeat. I spilled chicken fat on a pair of suede pants ( not sure why I was messing in the kitchen wearing suede pants, but that's another story!) Perhaps cornstarch would absorb the grease in your table.

Old English furniture polish (which this is) lists this product as an oil. It is possible/probable that you can leave it alone and the oil will eventually disappear with normal cleaning methods (hardwood floor cleaner such as Bona, Loba, Polywhey Cleaner, etc). Even a 'drop of dawn' soap in 1 gallon of water would do it. As mentioned above, a bit of bleach (5% solution on wood is about as exciting as you want to get) *might do it. If I'm correct and this is a temporary 'oil' then a mild degreaser (such as Windex original) can get rid of this stuff. I would be VERY cautious when using ANYTHING other than a wood floor cleaner. Personally I would dampen a clean cloth with the Windex and then LIGHTLY DAB at a bit of the dark colour. I would check the clean cloth to see if there is any 'old english' that is coming up. If it is, I would continue to be very gentle with the removal. And for the record, these 'oil' based products can cause damage to wood floors to the point where they may not be refinished in the future. That would be a TERRIBLE upset to someone who just wanted to make their floors look 'a little better'. You currently have a CLEAR finish over the wood. To get rid of the LOOK of nasty scratches (from dragging things across the floor), you can work with a FINISH pen. Yep. Home Depot, etc carries many versions of Finish pens. These are pen-like containers filled with URETHANE. You use them like a stain-pen...except there is zero colour. All you have to do is match the gloss level of your floor and voila you have a 'cure' for damaged finish. And the good thing about finish-pens is: they do NOT damage the wood nor cause any issues with future refnishing. Anything 'oil' (ahem...Murphy's Oil Soap, oil soap of any kind, 'eco' cleaners of any kind, etc, etc, etc) can and will contaminate the WOOD underneath to the point that future refinishing *could be made impossible.