If jobs or schedules are owned by a user account and that account is deleted, the job or schedule will fail to run.
When creating a new job in Management Studio, by default it will make the current logged in user the owner of that job. I suggest that on job creation, the owner should be changed to sa, as that account is likely to always be available.
I have not yet found any security implications from having jobs owned by sa, but please comment if you are aware of any.
If you inherit a number of jobs/schedules not owned by the sa account, there are a couple of scripts below to generate the proc calls to change the owners of the offending jobs & schedules. (This is for SQL2005 upwards)
-- Change job owners to sa
SELECT 'EXEC msdb.dbo.sp_update_job ' +
' @job_name = ' + char(39) + sj.[name] + char(39) + ',' +
' @owner_login_name = ' + char(39) + 'sa'''
FROM sysjobs sj
LEFT OUTER JOIN sys.server_principals sp
ON sj.owner_sid = sp.sid
WHERE sp.name != 'sa' OR sp.name IS NULL
ORDER BY 1
-- Change schedule owners to sa
SELECT 'EXEC msdb.dbo.sp_update_schedule ' +
' @schedule_id = ' + CAST(s.schedule_id AS VARCHAR) + ',' +
' @owner_login_name = ' + char(39) + 'sa'''
FROM sysschedules s
LEFT OUTER JOIN sys.server_principals sp
ON s.owner_sid = sp.sid
WHERE sp.name != 'sa' OR sp.name IS NULL