Residual noise in the BOLD signal remains problematic for fMRI - particularly for techniques such as functional connectivity, where findings can be spuriously influenced by noise sources that can covary with individual differences. Many such potential noise sources - for instance, motion and respiration - can have a temporally lagged effect on the BOLD signal. Thus, here we present a tool for assessing residual lagged structure in the BOLD signal that is associated with nuisance signals, using a construction similar to a peri-event time histogram. Using this method, we find that framewise displacements - both large and very small - were followed by structured, prolonged, and global changes in the BOLD signal that depend on the magnitude of the preceding displacement and extend for tens of seconds. This residual lagged BOLD structure was consistent across datasets, and independently predicted considerable variance in the global cortical signal (as much as 30-40% in some subjects). Mean functional connectivity estimates varied similarly as a function of displacements occurring many seconds in the past, even after strict censoring. Similar patterns of residual lagged BOLD structure were apparent following respiratory fluctuations (which covaried with framewise displacements), implicating respiration as one likely mechanism underlying the displacement-linked structure observed. Global signal regression largely attenuates this artifactual structure. These findings suggest the need for caution in interpreting results of individual difference studies where noise sources might covary with the individual differences of interest, and highlight the need for further development of preprocessing techniques for mitigating such structure in a more nuanced and targeted manner.