Marine sedimentary records are a key archive when reconstructing past climate; however, mixing at the seabed (bioturbation) can strongly influence climate records, especially when sedimentation rates are low. By commingling the climate signal from different time periods, bioturbation both smooths climate records, by damping fast climate variations, and creates noise when measurements are made on samples containing small numbers of individual proxy carriers, such as foraminifera. Bioturbation also influences radiocarbon-based age-depth models, as sample ages may not represent the true ages of the sediment layers from which they were picked. While these effects were first described several decades ago, the advent of ultra-small-sample $^{14}$C dating now allows samples containing very small numbers of foraminifera to be measured, thus enabling us to directly measure the age-heterogeneity of sediment for the first time. Here, we use radiocarbon dates measured on replicated samples of 3-30 foraminifera to estimate age-heterogeneity for five marine sediment cores with sedimentation rates ranging from 2-30 cm kyr$^{-1}$. From their age-heterogeneities and sedimentation rates we infer mixing depths of 10-20 cm for our core sites. Our results show that when accounting for age-heterogeneity, the true error of radiocarbon dating can be several times larger than the reported measurement. We present estimates of this uncertainty as a function of sedimentation rate and the number of individuals per radiocarbon date. A better understanding of this uncertainty will help us to optimise radiocarbon measurements, construct age models with appropriate uncertainties and better interpret marine paleo records.