The Blue Cross.

-When Valentin was having breakfast he noticed that the sugar was in the salt-cellars (salt-shakers? Sorry if this is right- it could be an American or Australian term- but I've personally never heard it) and the salt in the sugar-basin, and when he asked the waiter why did he did that, the other replied he didn't, that it did was a priest. To Valentin it seemed suspicious so he decided to follow the priests.

-When Father Brown knocked over the apple cart he did it as another track for the three policeman so that they would go on following the tracks. ('tracks' seems like a strange word choice here: 'trail' might be better?)

-The fact that Father Brown had broken the window allows to Valentin to continue with the chase.

-In the sweetshop the lady at the counter tells Flambeau that one of the priests has misplaced a parcel and he later returned claiming it, and asking that it be sent on to an address if found. The shopkeeper says to Valentin that the two priests were headed for Hampstead Heath, and with this information Valentin is capable to continue with the pursuit. (he is 'able to continue' or 'capable of continuing')

-In the park Valentin can closely follow the two priests. Hidden behind the trees he is capable to hear the conversation between them and find out the truth about them.

-The three of them have an objective, for get to achieve it they act in a clever way; Flambeau pretending to be a priest for to steal the parcel, Valentin following the tracks to catch Flambeau, and Father Brown acting as if he didn't know who really was Flambeau really was and what he wanted while he was letting tracks (leaving trails?) that allows Valentin to follow them. They use astuteness and intelligence with the goal of achieving their purpose.

-Father Flambeau is the character I feel I know best because I believe that what he does in the story, pretend be ignorant of the truth, is something that everyone does at least one time in their life; maybe not with the same objective, it's possible that we hide the truth from others to not hurt them, but all of us do it. Father Brown is also one of the characters I like the most. I prefer his character because he doesn't boast about his skills, is patient, and use the acquired knowledge. For example, he use his experience as a priest when he states a reason why he knew Flambeau was not a priest: "You attacked reason. It's bad theology."

-The kind of narrator is a third person who is not involved with the story and is not a character within the story. In this case, the narrator has a subjective narration describing Valentin's thoughts. The narrator's knowledge is limited to that character, it means that the narrator can't describe things unknown to the principal character. The narrator is given detective Valentin's point of view.

Hi! Well done with this! :) Your English is good and understandable! A few of the sentences seemed odd to me, particularly at the start, but as I said, I think some of it might just be because I'm not familiar with the subject!