The standard aggregate function array_agg() only works for base types, not array types as input.
(But Postgres 9.5+ has a new variant of array_agg() that can!)
You could use the custom aggregate function array_agg_mult() as defined in this related answer:
Selecting data into a Postgres array
Create it once per database. Then your query could work like this:
SELECT use.user_sched_id, array_agg(se.sched_entry_id) AS seids
      ,array_agg_mult(ARRAY[se.min_crew]) AS min_crew_arr
FROM   base.sched_entry se
LEFT   JOIN base.user_sched_entry use USING (sched_entry_id)
WHERE  se.sched_entry_id = ANY(ARRAY[623, 625])
GROUP  BY user_sched_id;
There is a detailed rationale in the linked answer.
Extents have to match
In response to your comment, consider this quote from the manual on array types:
Multidimensional arrays must have matching extents for each dimension.
  A mismatch causes an error.
There is no way around that, the array type does not allow such a mismatch in Postgres. You could pad your arrays with NULL values so that all dimensions have matching extents.
But I would rather translate the arrays to a comma-separated lists with array_to_string() for the purpose of this query and use string_agg() to aggregate the text - preferably with a different separator. Using a newline in my example:
SELECT use.user_sched_id, array_agg(se.sched_entry_id) AS seids
      ,string_agg(array_to_string(se.min_crew, ','), E'\n') AS min_crews
FROM   ...
Normalize
You might want to consider normalizing your schema to begin with. Typically, you would implement such an n:m relationship with a separate table like outlined in this example:
How to implement a many-to-many relationship in PostgreSQL?