Any user can get a listing of the projects or sources that were observed by ALMA on any given date with a simple query to the ALMA Data Archive, accessed from the Science Portal by following the left menu link "Data → Archive", and clicking the "Archive Query" button (or directly at http://almascience.org/aq/). Enter the desired date or date range into the "Time: Observation Date" field. Unselect the checkbox "Science observations only" if you are also interested in calibrator observations.
To get a listing of observed projects instead of the observations which are selected per default, select the "project" option in the "Options: Results view" field.
The query will return a list of projects or targets that were observed on the specified dates and which passed the zeroth level of quality assurance (QA0 - see the ALMA Technical Handbook). Keep in mind that these data may subsequently be judged inadequate for use in meeting the science goals specified by the proposer.
Additionally, Principal and Co Investigators can check the status and observing activity on their own projects by using the SnooPI Project Tracker, accessed from the Science Portal by following the left menu link "Observing → SnooPI" (or directly at http://almascience.org/observing/snoopi). See the SnooPI Manual linked to from the same webpage for more details.