According to Huygen's principle each point on a wave front acts like a source of light. If this is true, i think light waves coming from different sources (i.e points of a wavefront) must undergo interference giving rise to bright and dark fringes. Then Why do we need slits or gratings to produce interference?
Huygen's principale indeed says what you have mentioned, but be careful: each point of the wavefront behaves as a point like source of light. All these spherical waves do interphere together. That's the way the following wavefront is generated: it is the superposition of all the spherical wavefronts. In other words, the interpherence pattern related to this phenomenon doesn't allow dark regions. If you want to observe a typical interpherence pattern, with bright fringes and dark fringes, you need, for example a wall with two slits. When the wavefront impinges against the wall, all but two spherical waves that originate in each point of the wavefront are blocked by the wall. The two spherical waves that survive are those ones centered in correspondance of the slits. These two coherent spherical waves interphere and generate a typical pattern.
According to Huygen's principle :
All points on the wavefront act as a source of new disturbances and these new disturbances are collectively know as secondary wavelets
The tangent drawn to these secondary wavelets in their forward direction of propagation gives the position of new wavefront. (Although existence of a backward wave has been proved, but it is way too advanced right now)
BUT There are certain conditions which need to be satisfied in order for interference of light to take place :
Light wave emitted from an ordinary source (like a sodium lamp) undergoes abrupt phase changes in times of the order of 10^(-10) seconds. Thus the light waves coming out from the two independent sources of light will not have any fixed phase relationship and would be INCOHERENT and hence the intensities on the screen would add up. Therefore British Physicist Thomas Young used an ingenious techniques to "LOCK" the phases of the waves emanating from S1 (Source 1) and S2. He made two pinholes very close to each other on an opaque screen. These were illuminated by another pinholes that was in turn, lit by a bright source. Thus, S1 and S2 were now behaving like two coherent sources.
This is the reason why we don't encounter interference in our day to day lives.
Also, the condition of sustained interference is a difficult one to be produced.
If your question relates to monochromatic light, the answer is simple: You're right, interference occurs everywhere. Shine a laser beam at a spot on a wall in a dark room and observe the speckle pattern that lands on all the other walls. That is interference, resulting from each point on the irregular wall within the spot being at a different height and thus re-radiating the laser light with different phase. Each such point acts as a new source radiating in all directions. If the spot is very large, the speckle pattern on the walls gets very fine-grained, to where it may not be visible at all without a microscope.
If your question relates to white light, the answer is still that you're right, interference occurs everywhere. The speckle pattern described above still occurs, if you only look at single wavelengths. However, the speckle patterns for all the wavelengths are overlapped if you look at them together, and the patterns blur as a result.
So: we do not need slits or gratings to produce interference.