Managers at East Kent Hospitals University NHS Foundation Trust said they shared the figure with staff in order to improve services.
One woman, Vicki Adams, of Canterbury, said she found a used dressing stained with blood or faeces in clean sheets.
The hospital said 1.625m items were sent to laundry in the three months and the error rating was 0.0027%.
Ms Adams said she saw many examples of dirt and uncleanliness, the most obvious being the discovery of the used pad stuck to her bed linen.
"It was revolting to see that. It made me feel sick and shocked," she said.
She said she wanted the trust to make sure it did not happen again and added: "Forty examples isn't a small number."
Sue Roberts, director of infection prevention and control, said: "As part of our value of being open and transparent, we recently alerted staff to the mishandling of clinical waste, which we take very seriously.
"We did this to ensure that clinical waste is disposed of correctly.
"Our own laundry processes 6.5m items a year and has very strict procedures to ensure that any clinical waste mistakenly sent to laundry is not included in clean linen sent back to wards."
Trust bosses also told staff the errors posed risks to staff involved with laundry processing.
The trust runs hospitals in Ashford, Margate, Canterbury, Folkestone and Dover.
Clinical waste has been found dumped in dirty linen 40 times in three months at a Kent NHS trust.