As I understand it, anyone who wishes to examine electronic and browsing history has to make an application under RIPA to specify the "target" they are investigating. Fishing investigations are not allowed under RIPA.
The information is not being examined in real time by Police or the other agencies - and you are qquite right, the full list is extraordinarily wide, but an awful lot of those agencies - eg Gambling Commission - carry out prosecutions, and in their case examination of data held by ISP's etc.. can be useful to prove a case.
The information held is not being accessed in real time. That would still need an Interception warrant from the Home Secretary.
I would also point out that the trigger for an examination of data would normally come from a already occuring investigation, or in the case of intecepts by GCHQ, from trigger words or phrases. These would not go to agencies but to Law Enforccement and Security and intellgience services.
Telephone data (mobile and landline) has been subject to applications for access by the assigned law enforcement agencies for a number of years before this law came into being.
I understand the unease people feel about this, but in all honesty if the Government had explained it better, had explained the mechanics better, I don't think it would cause so much suspicion.
As to the argument that says "if you've got nothing to hide, so go on, post your bank account details to this forum, or let the window cleaner film you in your bathroom" it's wrong to manipulate the average person's normal security concerns against their confidence that they are not doing anything illegal which is what people mean.
In other words people can say "I am not a criminal, I am not a terrorist, I do not hold extreme views on politics, so yes, I have nothing to hide, but of course my bank account details are my business, and I am confident no one is going to fish for details of my private business"
It's not perfect. I'd be a fool to say so. But it's not the utter diaster that some peope in organisations opposed to it are making out.