For the most part, notes should be treated the same as coins: if the "dirt" isn't actively damaging the note, leave it there.
Stickytape is always a no-no. The sticky stuff just won't come off without chemicals if it's left there for any length of time.
Washing a note is generally frowned upon. Pressing or ironing a washed note is certainly frowned upon, as this not only artificially "improves" the note's condition (removing folds and creases), it can accelerate the degradation of the paper, making it brittle.
Needless to say, other more powerful "washing" like dry-cleaning fluid, organic solvents, bleach etc. is also frowned upon; this can damage the original ink and paper, as well as the paper.
There's a whole industry in China, Hong Kong and Singapore based on buying low-grade notes, bleaching, washing, pressing them and then selling them back on
ebay for 10x what they paid. You can only spot them because banknotes have serial numbers. We see them on
ebay Australia all the time.
For an old, fragile note that could fall apart if "something" doesn't hold it together, there are things that can be done. For example, I have a cut-cancelled
Texas "redback" $5 that I think was repaired very well; the "tape" is paper, tissue-thin, very narrow and doesn't seem to be sticky. The tape was applied on the
Here's back of the note where it's less visible. The note was slashed in five places when it was cancelled and is made of thin, fragile paper. Without the tape, it probably wouldn't still be in one piece today.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis