Analysis.

(Remember: this analysis is particularly true about British language and culture, though mostly it is the same for other English-speaking countries like Australia and the United States.)

Sentence by Sentence analysis.

Peter: "So you are baby-sitting next month. Teaching the new boy all about it."
(Peter's use of language is slightly derogatory and patronising. He does not like the idea.)

Sally: "Well, we all have to start sometime. I just hope he's ok."
(Her worry is that Ivan will be someone she doesn't like. She is neutral about helping him.)

Peter: "Just as well I'm very busy this month, or old Barwell would have given the job to me."
(Peter wants to explain why Sally is supervising Ivan and not him. He suggests he would have been the boss' first choice.)

Sally: "Of course."
(Sally is not interested in discussing the matter.)

Peter: "So he's looking after the Walton portfolio. I don't see why Barwell couldn't have given that to one of us, and given the new boy something more routine. I could do with a new challenge."
(Peter is rather jealous of Sally's new responsibility and Ivan's portfolio. Notice how "one of us" becomes "I".)

Sally: "I thought you said that you were very busy this month?"
(Sally is finding Peter a bit irritating, so she shows him that he is contradicting himself.)

Peter: "I am. We may not all have high yeild portfolios like you do, but we all have things to do. I have some very interesting prospects at the moment."
(Peter is very defensive. He shows that he knows that Sally's portfolio is doing better than his, but he hints that this will change soon.)

Sally: "I wonder why this Ivan left Bellweather?"
(Sally doesn't care (and probably doesn't believe) that Peter has some interesting prospects. She is worried about Ivan.)

Peter: "They probably threw him out. Stealing other peoples work."
(Peter is worried that Ivan is going to take some work from him. He is negative towards Ivan.)

Sally: "Oh, calm down Peter - you have been complaining for ages about being overworked, and now that we have someone to share the work, all you can do is complain.
(Sally is not worried about Ivan taking her work. She thinks they have enough already. )

Peter: "It's all right for you. If the work slows down, it's not you who'll go - you're the boss' blue-eyed girl."
(Peter thinks that Mr Barwell prefers Sally's work to his.)

Sally: "I have just had a few good months - it will be your turn soon."
(Sally tries to explain her success in a way that won't make Peter jealous.)

Peter: "Yes, you are going to have to watch out for yourself and this Ivan - any mistakes of his, and you will be blamed."
(Peter is looking for a way to upset Sally, and make her feel bad about supervising Ivan.)

Sally: "Oh, dear, do you think so?"
(Sally has not thought of that. Now she is worried.)

Summary

Sally and Peter work in the same office with the same type of work. Sally is better at the job than Peter. Peter often complains, and he does not like it when other people do better than he does. He also thinks he is more important than Sally, and he should have got the job of looking after the new person. Sally does not like Peter very much, and she is worried that if Ivan is like Peter the two men will work together against her. She is not worried about Ivan doing better than her at work, because she knows she is good at it.