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The question is not about the slightly differing wavelength of the devices caused by manufacturing processes or the shift from changing temperature.

A German source says that the spectral width with which laser diodes emit their light is only 1 nm, in the case of the Distributed Feedback Laser (DFB) it is only 0.1 nm. (“Die spektrale Breite mit der Laserdioden ihr Licht aussenden, beträgt nur 1 nm, im Falle des Distributed Feedback Lasers (DFB) ist sie sogar nur 0,1 nm.“) Could I suppose that a cheap laser pointer has a bandwidth of more than 1 nm?

The bandwidth of a sodium-vapor lamp has two spectral lines very close together at 589.0 and 589.6 nm. This turns out that the bandwidth of this lamp is around 0.6 nm?

For the background see this question about The function of the pinhole in the double slit experiment and therein the comments below the answer.

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The two lines in a sodium lamp can be separated (e.g. with a diffraction grating) and typically have linewidths of around 0.05nm (see measurement).

Different types of lasers have different line-widths (as you have already seen). By 'laser pointer' you probably mean a cheap laser diode (although you could also mean a diode pumped solid state laser). In a typical fabry-perot package(L=1mm, n=3.5) the longitudinal modes are spaced by roughly 0.1nm. You can force the laser to operate in one mode by feedback or by controlling the temperature/current. More likely your laser pointer will be operating in many modes at once.

At any rate all of these things will be sufficient to perform double-slit experiments. In a double slit experiment light from two slits $d$ apart (the slits are assumed to be much smaller than $d$ and larger than $\lambda$) interfere to after a distance $L$ to make maxima space by $\delta=L\lambda/d$. If you have multiple wavelengths then these will all diffract but with slightly different phase shifts (and thus spacing). But the relative shift in $\lambda$ is so small you should have no worries about fringes `running into each other' as it were.

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