The kettle shown in the opening scene whistles as it boils, increasing in volume and pitch until the gas underneath it is turned off. However the kettle has a normal spout - not a whistle - and should not be whistling at all.
Whenever Angela draws her weapon, there is a sound of the hammer being cocked. The Smith and Wesson 6906 has a "bobbed" hammer, no "handle" to get your thumb onto easily. Cocking the weapon is difficult, especially since her thumb never goes near it. It's also policy for most police departments to fire the first shot without cocking the weapon first. In some departments, not following this policy is grounds for immediate dismissal.
When Father Hennessy is drinking himself to death in the liquor store the first two bottles he grabs are wine bottles. We hear the tell-tale sound of a cork popping, but not only would it be physically impossible to pull out a cork, that had not been previously opened, without a corkscrew, all corked bottles are sealed with foils, which we also don't see him removing. While there are cheap wines that have a twist-open top, the cork sound is an error.
The priest tells Angela that suicide is a mortal sin and therefore Isabel cannot have a Catholic funeral. While the church does still consider suicide a sin, this judgment does not hold in cases of mental illness. In modern times, suicide is considered evidence of mental illness, and since Isabel was in a mental institution, whether or not she may have a Catholic funeral is a moot point. People who commit suicide are no longer refused a Catholic burial in consecrated ground.
When in the car about to call Beeman, Constantine says that the bible in hell gives a whole new meaning to "Revelations". The last book in the Bible is actually "Revelation", without the 's', as its story is considered to be a single "revelation." (This mistake is common in real life.)
When John, Angela and Beeman are discussing the Bible passages about the Son of Satan, Angela says "There's no 17th Act in Corinthians" and he replies that the Bible in Hell has more "acts." The Bible is traditionally divided into chapters, not "acts".
When Angela goes to see Isabel's body, the clock on the wall over the pool reads 6:45, yet in the same scene Angelas watch appears to read 3:45. Then, at the elevator with Constantine, the clock reads 3:40.
When Angela and Constantine are speaking, he is smoking a cigarette and he traps a spider under a cup with smoke. In the next shot, the cup and the spider are gone from where they were set and in the shot after that, it's in a completely different spot on the table.
Constantine traps a spider with a glass and blows some cigarette smoke into the same glass. Later, Angela lifts the glass, releasing the spider. There is considerably more smoke in the glass when the spider is released.
When Angela is vomiting after the first demon attack on her, she begins by vomiting into the corner next to the pillar on the right of the visage of Christ, but when the angle changes she's now vomiting directly in front of the visage, facing the opposite direction.
When Angela is in submerged in the bathtub, she struggles vigorously with John, causing water to splash about. As she crosses over and time slows, a drop of water can be seen falling, however, into a perfectly still, ripple-free bath.
In one scene Chas is seen melting down gold jewelry to make bullets on a stove top in a small skillet. This however is not possible as a stove could never produce enough heat to melt gold in this fashion.
When Constantine enters the bowling center, we see all of the lanes; however, when Constantine goes into the machine area, the machines are not bowling machines; and there is a walkway between the backs of the machines. The bowling center was one location, while the machines were in another location.
The Spear of Destiny was taken by Adolph Hitler at the start of the anschluss of Austria. The opening scene features the Spear being unwrapped from a Nazi flag, hence indicating it was the Spear taken from Austria. However, while the Spear and other artifacts were very nearly lost or destroyed at the end of WWII, they were rescued and the Spear returned to Austria. See the first episode of "Myth Hunters" for details.
In the beginning where Constantine is exorcising the little girl, the mirror gets pulled out of the window. The line used to pull the mirror out can be seen clearly attached to it but, in the next overhead shot when it is falling toward the car, the line is clearly no longer attached.
When Angela is looking at the video of Isabel's suicide, she rewinds it, but the button she pushes on the far left is not the "rewind/search" button on QuickTime Player, but instead the "return to beginning".
Near the end, when Kramer is proceeding to place the blessed cross into the emergency sprinkler system, he shoots a hole into a section of the top of the tank. Firstly, it is highly unlikely he would be able to blast a perfect circular hole into a (steel?) water tank meant to supply a building's fire sprinkler system with a shotgun, even with magnum buckshot or special blessed rounds. Secondly, if he was able to, the diameter of the hole Kramer actually makes is nowhere near wide enough for the cross to fit, no matter how he manipulates it. Hence, the camera simply cuts away to the cross dropping into the tank.
The goof items below may give away important plot points.
When Constantine decides to cut his wrists so Lucifer comes for his soul, the blood spills and touches his Oris watch on the floor and time stops. On the next scene, from above, the blood pool is smaller and doesn't touch the watch. The next scene, taken from below, the watch is again in the blood pool.
When Constantine cuts his wrists he bleeds to death in just about one minute, while in reality that method of suicide is actually quite slow (and there's no forward jump in time during that minute as can be seen by Gabriel's simultaneous actions). However, with the supernatural involvement in the whole scenario, we can be lenient.