Peterborough United and Walsall both had valid claims for a penalty kick in the second half, but Darren Ferguson's men will be satisfied with the point after a goal-less draw at the Bank's Stadium.
Adam Chambers fired wide with the first effort of the game, the Saddlers skipper dragging his right-foot shot well wide of Ben Alnwick's goal.
Romaine Sawyers dragged a shot wide of the far post on 13 minutes as both sides exchanged good moments in wide areas without an end product.
Sawyers missed his kick at the back post on 21 minutes after a deep Taylor cross as the hosts enjoyed a fair share of possession.
On 27 minutes, Posh were close to the breakthrough as left-back Kgosi Ntlhe, returning to the starting line-up after a long spell on the sidelines with a hamstring injury, sent a swerving shot inches past the upright.
A shot from Taylor was deflected wide for a corner kick on the half hour mark with the resulting set-piece causing plenty of problems before Chambers' hacked it clear.
Burgess saw a header hacked off the line by Taylor after a free kick from the Posh namesake moments later after Vassell had needlessly been felled.
Bostwick was next to try his luck for Posh as Newell stood up an excellent cross to the back post, but the former Stevenage man planted his header wide of the post.
Alnwick tipped over a curler from Forde on 40 minutes as Posh afforded the midfielder plenty of room to take aim from distance.
Cook was booked for a bad challenge on Ntlhe which provoked a disagreement with both sets of players. Newell and Sawyer were both booked by Mr Woolmer.
Forde flashed a shot wide of the near post after cutting inside onto his left-foot from 25-yards. Sawyers fired wide when well placed on 61 minutes ass Posh made a first change with Mendez-Laing replacing Taylor.
A Michael Bostwick free-kick went wide on 70 minutes after Vassell had been upended 30-yards from goal. Alnwick produced a fine stop with his legs to deny Sawyer on 84 minutes.
Walsall were screaming for a penalty as Santos unintentionally handled the ball following a long ball forward, but nothing was given. Substitute Grimes then headed wide at the back post.
Posh were screaming for a penalty themselves in injury time as a long throw from Newell appeared to strike the arm of Chambers but nothing was given.
Walsall: O'Donnell, Purkiss, Taylor, Downing, A.Chambers, Sawyers, Cain, J. Chambers, Cook, Forde (sub Benning 84min), Manset (sub Grimes 78min). Unused subs: O'Connor, Baxendale, Flanagan, Clifford, MacGillivray.
Posh: Alnwick, Smith, Ntlhe, Burgess, Santos, Bostwick, Payne (sub Anderson 77min), Taylor (sub Mendez-Laing 61min), Newell, Washington (sub James 77min), Vassell. Unused subs: Henry, Oztumer, McCann, Ferdinand.
Half-time: Walsall 0-0 Peterborough United
Full-time: Walsall 0-0 Peterborough United
Attendance: 5,495 (579 Posh fans).