This year's fruiting canes will start to die off but not quite this fast or dramatically. Yellowing leaves is usually a sign of nutrient deficiency so something like pelleted chicken manure or an aged manure slurry applied with a nozzle-removed watering can should help. Any of the sulphate additives will also help green up the leaves as well as nitrogen based ones. It could also be the water they get, if any. Raspberries are very thirsty plants during production times and tap water is too alkaline for them. If that's all you have, then add a few tablespoons of plain vinegar to the water can as raspberries prefer more acidity but not to the level of blueberries. Acidity will help unlock availability of nutrients to the roots.
Also, if you've added any mulches like fresh grass or wood chips, they'll rob the nitrogen from the soil to decompose. Straw and some peat moss mixed in are better as the peat will help lower the pH.
As for the moldy berries, raspberries ripen quickly and just as quickly turn, so you'll need to be more diligent at picking. After the season finishes, dig deep in a few trouble areas to see if there's a drainage problem or rubbish blocking the roots or whatever. I found a big anthill in one area causing trouble for me.
In fall, give the whole raspberry area a nice layer of aged manure with a dusting of ammonium sulphate and it will have the winter to sink in and be ready for next season's growth.
Here's a bit more info:
http://www.gardenersworld.com/how-to/problem-solving/raspberry-nutrient-deficiency/