I am thinking of using a diffuser on my canon speedlight flash to soften harsh shadows when shooting indoors. I was wondering what the disadvantages of this might be.
It will reduce the total amount of light that your flash can put out. It will also use more power for the same amount of light hitting your subject.
When indoors, if your flash can bounce/swivel but the wall is further away, you will probably be better off bouncing without a diffuser.
Harsh shadows are due to a small apparent light source (light travels in a line, soft shadows are when the transition from light to dark is gradual and the object can see part of the light source).
Adding a diffuser barely (e.g. stofen) or doesn't at all add to the size of the light source. The exception is that when walls and ceilings are close, the light is diffused and sent to those surfaces which can create a bit of a larger light source.
Note that when you bounce a flash, it can give a color cast based on the color of the surface.
I'm not sure you can call it a disadvantage as such, but they will usually reduce the overall amount of light, so you have to consider that when metering your subject. The light loss will vary, so there's no hard and fast answer to what you may need to compensate. Anyways, a good source for information on diffusers can be found on this site, including tips on how to use them to best effect.
Anyways, in a nutshell, there isn't really any disadvantages if they're used for the purpose they're intended for.
There's only one disadvantage that it may not have the effect you are looking for.
A diffuser spreads the light in more directions than the flash illuminates without the diffuser. Reasons why this might be unhelpful include:
People often assume that a diffuser softens the light in an image. This is not really true. Or at least, it's a secondary effect. The softness of the flash lighting in a photograph is determined by the apparent size of the light source as seen from the position of the subject. Diffusers soften light (when they do it at all) mainly by causing the light to be partly reflected from the flash off other nearby objects before hitting the subject, thus increasing the area from which illumination comes.
An alternative technique is to angle your flash head up or back, and put a card or sleeve (a "gobo") on the flash to prevent all direct illumination from the flash hitting the subject. Thus the light source is now the reflection from the ceiling (which is large) rather than the flash itself (which is small) and so the lighting is softer.
The best book I've read on this subject is On-Camera Flash Techniques for Wedding and Portrait Photography by Neil van Niekerk.