Single slit experiment Suppose we are doing a double slit electron diffraction experiment and we place a detector behind the slits to detect which slit the electron passes through. If we do this the diffraction pattern will be destroyed and instead we get just two peaks - one behind each slit.
Suppose we use just one slit, then we would expect to get a diffraction pattern described by the $\mathrm{sinc}(x)$ function, as shown in the figure below.

Now suppose we place a detector behind the slit just as we could do in the double slit experiment. Will this also destroy the diffraction pattern leaving just a diffuse band?

 A: If the detector is capable of revealing which part of the slit the electron passes through, even the single-slit diffraction pattern will disappear.  Any diffraction pattern depends on uncertainty about the paths of the detected particles.  Remove that uncertainty, and the diffraction pattern disappears.
A: The "diffuse band" that you mentioned is just what people talk about to simplify the thought experiments. Either they do this by ignoring the peripheral bands, or they assume the detectors are infinitely precise. This is done because the discussion is about what happens to the middle band of light. 
In reality you will always get either a single-slit pattern or a double-slit pattern, and really all experiments are centered around whether or not the middle band of the single-slit pattern gains extra fringes within it. 
If there are no detectors, we get a double-slit pattern (the two single-slit patterns interfere with each other). If there is a detector, we get single-slit patterns (the two single-slit patterns don't interact). 

So with detector present or not a single slit will always produce interference pattern with small lateral waves?

If the slits openings are not infinitely small and the detectors are not infinitely precise then yes, but see S. McGrew's answer for a caveat. 
A: For a detector you would need either real photons or virtual ones as part of the detection process. Any interaction with the electron after is passes the slit allows the electron to "recalculate" its path, this new path is now not involving the slit at all, therefore NO pattern.  It is the same for the double slit.
It is the whole setup (source + slit(s) + target) that influences the possible paths of a photon or electron, in dark areas there are no photons/e, bright areas have them all.  The tight geometry of the the DSE or SE is what limits the paths and shows the pattern (p.s. the word interference is very historical and somewhat misleading). High probability paths are ones where the path length is related to the wavelength.
