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my friend reported this problem when he fitted a bigger tyre by raising the suspension and when he reverted back to the stock tyres the problem was solved.
Assuming that you are using the stock tyres the problem may have something to do with your rear suspension.

plz tell us in detail .........

what do you exactly mean by stability in question..........

and describe in detail.....how is it shaking.....from where..etc etc...

have your rear tyre checked at a proper tyre shop.

it's quite possible that the tyre hasn't been installed well on the rim.

This problem is similar to what i have faced . At the speeds over 50 the rear wheel was wobbling like hell. In my case the swing arm bush was the culprit !
Put your bike in center stand and check whether the wheel has play in sideways . If it shakes then stay/swing arm bush is gone ! BTW has your bike faced any fall ?

^^ what when the front wobbles? what to do then? I have been having this problem for sometime now.

I had that one too ! IT could be either worn out cone set bearings or unequally worn out tyre ! or even bent forks ! IIRC it costs around some 370 rs and stay/swing arm bush change 125 rs.

Check the pressure in tyre regularly
Always maintain the air pressure in tyres.

You said that the tyre was punctured right
You have not mentioned that how big that puncture was(a broad big nail or a small splinter etc,multiple puncture or single)
Has that mechanic put some tube/small piece of tyre inside between the tube and tyre.Mostly mechanics do this if the hole in tyre is slightly big cause due to a broader nail. because in this case the tyre surface is not uniform everywhere hence it will wobble.If mechanic has done this thing then I think that your bike will give you this problem till you change that tyre.

If that puncture is not big one then I think that after removing puncture there is some misalignment in fitting back the tyre
So you can check with some good tyre alignment centers where computerized wheel balance is done or you just show it to the Bajaj Authorized service center.He may tell you from where the tyre alignment can be done.

If it is properly aligned and still you get this problems then I think that there is slight bend in the alloy wheels but that will cost more since removing bends in alloy wheels is a tough job/rather impossible one.