A couple of points to add.
Yes absolutely you can record a meeting if you so wish and can do so in a way that is not disruptive. But, from a legal perspective, the only record of a meeting that will be accepted in law as an accurate record of proceedings is that written record, the Minutes, that are signed by the Chair to confirm their accuracy. That is not a "clerk thing" that people seem to imply, but is based upon statute and case law. If follows therefore that the written record needs to be accurate but it does not need to be verbatim. Why a decision is taken can add useful context but the actual resolution is the most important part.
In the process of agreeing the written record, this is a process requiring a resolution of all councillors so there should be a vote on accepting the accuracy of the minutes. If you are presented with a draft which you do not feel accurately reflects the meeting to which it refers, you can/should challenge this. Amendments should be put to the meeting and agreed by the meeting as a whole. It doesn't really matter whether that draft you are amending is solely the work of the clerk (although clearly that is their job) or whether the draft presented to you is a collaborative effort. It is a draft until agreed by members.