Seen to be working as a team

[missingleg]

What do you do if your colleague holds a different opinion from yours and takes action before consulting you?

For instance, your partner (wrongly) calls no-ball for a full-toss at the striker's end, but you believe it was a legal delivery, and a catch is taken.

Or it's raining and your partner tells the players we're going off when you don't think it's unreasonable to continue

What if you think an incident warrants a report but you find out your partner has already told the guilty parties that as far as he's concerned, he's willing to forget it?

What if you know your partner has got the law wrong and the players ask you for a second opinion?

As you should be (and be seen to be) working as a team at all times, would you give in and pretend to agree with your partner? After all, the alternative would not be ideal whatsoever.

[jaybee]

Very difficult. Looking at it from one angle what would you expect if you got it wrong?
If the striker's end umpire no-balls a beamer he doesn't know what he's doing and odds are that he won't follow the proper warning procedure. As the call could have been for any other reason and there's no specific authority for retracting the call I don't think you can give the catch out - but that's not down to you; you can't second-guess his decision in the same way you can't query his decision on a stumping. This is a case where it's wiser not to ask until after the match is over.
If the players ask you for a second opinion in this sort of case you should perhaps dissemble by saying that he's the judge.
The other two examples are of cases where the umpires should confer and reach a joint decision so it's that much harder to let it go.
As far as Ground Weather and Light are concerned there's a bit of wriggle room but it depends on just how bad - or even biassed - the colleague's judgment is. If I could find a way to go along with it I'd do so but want to discuss it fully in private off the field.
On disciplinary matters however I think you should stand your ground. The first stage has to be for the umpires to confer and usually the result - if they agree - is to make the skipper aware of his responsibilities. If your colleague has intimated that he's OK with it without consultation that's clearly wrong; after talking to him I think you would be justified in reminding the captain of his duty to ensure that all's within the spirit of the game even if he's not of the same mind.
Page 128 of the Open Learning Manual - dealing with unspecified unfair play (Law 42.2) says:

If either umpire considers that an incident constitutes [an] unfair act he must call and signal Dead ball. Law 42.18 sets out the procedure thereafter
tell the other umpire
both will inform the player’s captain
instruct the captain to take action
indicate to him that the offence is a serious one
tell him that it will be reported
both will make a joint report of the incident

It's clear from this that it's to be regarded as unfair even if only one umpire think's it is. The other umpire should then back you up.

If there is a difference in how seriously he regards it he can always include his views in the report that has to be made. As the ECB and leagues are very concerned to eliminate as much poor behaviour as possible I would put money on the action taken being backed up in the vast majority of cases.