Why does a CD work as a diffraction grating even with light from a light bulb? I have a really hard time solving the following problem I accidentally came across today.
Looking at the back of a usual CD one sees coloured bands. This is explained by the fact that the surface (pits and bumps) is effectively a diffraction grating.
But why is this effect already visible when one uses incoherent light, e.g. from a light bulb, whereas the interference pattern of a single or double slit would be missing with such illumination?
 A: Coherence is not a yes/no thing. Different sources of light have different coherence lengths. At distances shorter than the coherence length, there are correlated phases. At greater distances, the phases are uncorrelated. In the double slits we use at my school for a student lab, the distance between the slits is 0.6 mm. On a CD, the sizes of the pits and bumps is on the order of 0.001 mm. I think most common sources of light have a coherence length that is between these two numbers, so you get diffraction off of a CD, but not with double slits.
A: Anything with a repetitive small structure can create diffraction patterns,   If you shine a light on to an LP phonograph record, you will see a bright light pattern off the grooves on the disc.  It can be shown that the width of the bright pattern is proportional to the recorded transverse velocity of the signal.  The pattern on a CD is also a function of what is recorded, but due to it being digital information, it is not as recognizable as the analog information on LPs.
A: As pointed out by George E. Smith, interference effects have been obtained for centuries.
Historical
Newton's rings are an example of interference fringes. Among the most famous experimental results in the history of physics is Young double slit setup. Using sunlight as a light source interference fringes were obtained. 
The difficulty with using sunlight is the following: the light must come as if from a point source. The light that reaches the two slits must have passed through a small aperture, and that aperture must be very small relative to the distance between aperture and the double slits.
So, for a practical setup you're down to a pinhole, and that means you have very low luminosity. That makes it hard to actually see the interference fringes.
Also, for different wavelengths of light the spacing of the intereference fringes is different. So with sunlight only a few central fringes will be actually visible. The further from the center the more the fringes from the different wavelengths will overlap, washing them out.
The following features of laser light make it especially suitable for interference setups:


*

*The light is very close to  monochromatic

*You use a laser device that has the laser light exiting the laser cavity through a very small aperture (in effect a point source of light).


To obtain interference fringes those two are sufficient.


Astronomy
In astronomy spectra are obtained with diffraction gratings. 
To study the spectrum the starlight must be separated by wavelength. A prism will do that, but nowadays a diffraction grating is used, so presumably that gives better results.
Stars are in effect point sources, that is why a diffraction grating can be used to obtain the spectrum.


CD as diffraction grating
The spectrum-separating effect of a CD-as-diffraction-grating is so strong that it is highly visible even with a spatially extended light source. 


So, why do some authors mention 'coherency' in a way that suggests this 'coherency' is a crucial factor?  The problem is oversimplification. The generalized concept of coherency has quite a wide scope, and mentioning 'coherency' in a simplified picture will lead the reader astray.  
