An end-to-end game saw chance at both ends but neither side was able to break the deadlock.
Blackpool goalkeeper Matt Gilks produced a superb parrying save to keep out a Dexter Blackstock header just before half-time, while at the other end Lee Camp performed similar heroics when Thomas Ince nodded goalwards.
The draw helps both side's cause at opposite ends of the table.
Blackpool remain fifth but are now only two points ahead of play-off chasing Middlesbrough, who narrowed the gap with a 1-0 victory at Derby.
The point is perhaps more useful to Forest as they are now seven points clear of the relegation zone with just three matches remaining.
With Garath McCleary suspended, Paul Anderson returned to the Forest team to make his first appearance for six weeks. Fellow midfielder Jonathan Greening was also back in the reckoning after a month-long absence and started on the bench.
Barry Ferguson was recalled to the Blackpool starting line-up in place of suspended midfielder Keith Southern.
A second change by Tangerines boss Ian Holloway saw Gary Taylor-Fletcher come in for Lomana LuaLua, who was among the substitutes.
Blackstock had two early chances but failed to hit the target from good positions before Matt Phillips did likewise from the edge of the box for Blackpool.
Gilks denied Anderson midway through the first half before producing a brilliant save from a stinging Joel Lynch effort after 40 minutes.
Gilks was at it again to thwart Blackstock just prior to the break before Camp responded with an equally good stop to keep out Ince's header in the 55th minute.
Radoslaw Majewski perhaps should have given Forest the lead just after the hour mark but the Pole put his 12-yarder wide.
Gilks then smothered the danger following a couple of efforts from Anderson and Greg Cunningham late on.