That's a big shortcoming of sediments over the others. What you do is date material at intervals within the sediment, construct a chronology of depth to age, and look for anomalies. There is always going to be some mixing, bioturbation, etc. The idea is that most of it will average out on the longscale. Also, with sediments you usually are looking at a more coarse resolution of time. In other words, you are looking at "century" trends to rather than annual ones. This is also because there is a lag between vegetation and favorable conditions (trees have to grow, flourish, etc. before they start putting out pollen, and they don't just disappear or move right when conditions change), and thus a lag in what is in the sediments.
There are some sediments that have annual depositional patterns that make it possible to date to an annual basis, but even still they can't be exactly "placed in time." In other words, you can know they are annual, but you can't say they are 1377 until 1584 or something. But you can know they are roughly in that range.
Knowing things at a century or decadal level is good enough though, when you are talking about 1,000's of years ago. Doesn't really matter if it was a Tuesday or Wednesday, you know?
