slippage is known as flaring in an automatic box, if you are facing 2-3 shift flare then it is classic sign of worn out clutches in the the trans. You can get a full rebuild kit for it from nearly anywhere, Best would be to open up the trans and get good working replacement parts for the worn out stuff.
Most causes of failure in these transmissions is either lack of ATF change or using Type F or Type A ATF (the cheap ones). They make the transmission shift abnormally which then causes other failures.
for your manual transmission - before condemning it and rebuilding or replacing it - change the oil, use Caltes Delo 400 15W40 in it. it takes 2.2 litres. It is the only product you should use. Thick gear oill will cause the synchronizers to stall and eventually grind the gears. Change the gear oil every 2 years and whenever the car was dunked in rain water.
Do NOT use regular gear oil in your accord manual trans. It will cause very expensive repairs and will also cause the speed sensitive steering assist power reduction system to stop working.