The Latics dominated long spells but they remain bottom of League One and without a win in 10 games.
Vale's Ryan Taylor wasted an early chance before Oldham produced a counter-attack which ended with Freddie Ladapo being denied by visiting goalkeeper Jak Alnwick.
The hosts squandered a gilt-edged opening after 26 minutes as Ladapo was left with only Alnwick to beat, but the on-loan striker dragged his shot wide from 10 yards.
Vale went close through Sam Kelly, whose well-struck volley brought a fingertip save from Connor Ripley.
After the break Ladapo's latest attempt to break the deadlock saw him fire off target after good build-up play.
Vale were rescued by Alnwick in the 68th minute as he made a fantastic one-handed save to claw out Carl Winchester's header.
Ripley palmed away Taylor's late free-kick but Alnwick had the final say by touching Billy McKay's shot against the post.
Report supplied by the Press Association.
Match ends, Oldham Athletic 0, Port Vale 0.
Second Half ends, Oldham Athletic 0, Port Vale 0.
Attempt saved. Darius Osei (Oldham Athletic) left footed shot from outside the box is saved in the top centre of the goal.
Carl Winchester (Oldham Athletic) wins a free kick in the attacking half.
Foul by Kiko (Port Vale).
Corner,  Oldham Athletic. Conceded by Jak Alnwick.
Attempt saved. Billy McKay (Oldham Athletic) right footed shot from the centre of the box is saved in the bottom right corner.
Attempt missed. Carl Winchester (Oldham Athletic) left footed shot from a difficult angle on the left misses to the right.
Foul by Anthony Grant (Port Vale).
Billy McKay (Oldham Athletic) wins a free kick in the attacking half.
Attempt saved. Ryan Taylor (Port Vale) right footed shot from outside the box is saved in the bottom right corner.
Rigino Cicilia (Port Vale) wins a free kick in the attacking half.
Foul by Peter Clarke (Oldham Athletic).
Delay over. They are ready to continue.
Delay in match Jerome Thomas (Port Vale) because of an injury.
Foul by Ryan McLaughlin (Oldham Athletic).
Anthony Grant (Port Vale) wins a free kick in the defensive half.
Attempt saved. Nathan Smith (Port Vale) header from the centre of the box is saved in the bottom right corner.
Corner,  Port Vale. Conceded by Peter Clarke.
Attempt blocked. Rigino Cicilia (Port Vale) right footed shot from the centre of the box is blocked.
Attempt missed. Ousmane Fane (Oldham Athletic) left footed shot from outside the box is close, but misses to the right.
Anthony Grant (Port Vale) wins a free kick in the attacking half.
Foul by Ousmane Fane (Oldham Athletic).
Corner,  Oldham Athletic. Conceded by Nathan Smith.
Corner,  Port Vale. Conceded by Billy McKay.
Attempt missed. Paul Green (Oldham Athletic) header from the centre of the box is too high following a corner.
Corner,  Oldham Athletic. Conceded by Kjell Knops.
Darius Osei (Oldham Athletic) wins a free kick on the right wing.
Foul by Kjell Knops (Port Vale).
Attempt saved. Paul Green (Oldham Athletic) right footed shot from outside the box is saved in the bottom right corner.
Paul Green (Oldham Athletic) wins a free kick in the attacking half.
Foul by Rigino Cicilia (Port Vale).
Substitution, Port Vale. Chris Mbamba replaces Anthony de Freitas.
Delay in match Ryan McLaughlin (Oldham Athletic) because of an injury.
Foul by Nathan Smith (Port Vale).
Ryan McLaughlin (Oldham Athletic) wins a free kick on the right wing.
Foul by Jerome Thomas (Port Vale).
Peter Clarke (Oldham Athletic) wins a free kick in the attacking half.
Attempt saved. Carl Winchester (Oldham Athletic) header from very close range is saved in the bottom left corner.
Substitution, Port Vale. Kiko replaces Sam Kelly.
Oldham boss Stephen Robinson is under increasing pressure after his side were held to a goalless draw by managerless Port Vale.