I have imported point coordinates from a database, but I need to manually adjust a lot of the locations. Is there a way for QGIS to automatically update the point locations in the attribute table after you move your points?
Patrick, if you have brought the point data in from a non-spatially-enabled source, you will need to save to a new, spatially-enabled format (and load that into QGIS) before you start your editing.
After that, you'll want to use either the Move Feature(s) or Node Tool.
Once in edit mode for your point layer, make your adjustments with either of those tools, then either click the Save Edits button, or exit edit mode (which will prompt you to save edits). While editing the points, an in-memory attribute table is updated, then on save, written back to the data source.
Many edits are undo-able, but not all. Choosing to not save your in-memory edits will leave your data source unchanged.
Using Field Calculator $x and $y operators, you can over-write the old coordinates in attribute table. Just run it once - after you have moved all points to the desired locations.
Field Calculator v.2.x: http://docs.qgis.org/2.0/en/docs/user_manual/working_with_vector/field_calculator.html
Field Calculator v2.4+: http://nathanw.net/2014/05/23/qgis-field-calc-bar/