The orange spots are caused by a rust fungus (Phragmidium rubiidaei), also known as red raspberry yellow rust. The spots are clusters of hundreds of spores, which can be thought of as seeds of the fungus.
Rust fungi are plant pathogens that need to be on a living plant to survive, except for short periods of time when they may be dormant.
In New Zealand there are about 250 species of rust fungi, of which half have been introduced. One such recent introduction that has many people worried is the rust fungus Austropuccinia psidii. This fungus causes myrtle rust disease, which infects some of the myrtle plants in Aotearoa. Our native rusts grow in balance with their plants having evolved together for millions of years.
The red raspberry yellow rust has also been introduced to New Zealand. You initially see the yellow-orange spots in late spring to early summer on the leaves of the raspberry. There may be large numbers of spots (pustules) produced on a single leaf. In cases of severe infection, the leaves may be shed to protect the plant. In autumn and winter, the spots will become less noticeable and may be replaced by black spots that are the over-wintering spores.
The fungus can survive during winter in the fallen leaves and then reinfects the plant in spring. If you want to reduce the severity of the infection, you can remove the fallen leaves and/or prune the infected areas in winter before the growing season in spring.
In most cases, the rust will not kill the raspberry plant as it needs the plant to be living so that the rust itself may survive. For the most part, the rust will not affect the yield, so you may continue to enjoy raspberries — just give them a good rinse with water first.