Learn Hardcore Turkish: Broşürü okurken sloganı hemen fark ettim; akılda kalıcı. - While reading the brochure, I noticed the slogan immediately; it is memorable.

fark etmek: very common and neutral for “notice.”
farkına varmak: slightly more “to become aware/realize,” sometimes a bit more formal or cognitive. Another common alternative is dikkatimi çekti (“it caught my attention”).

Formation: verb root oku-
- aorist -r
  - -ken → okur-ken → okurken.
You may also hear okuyorken (present continuous stem okuyor
- -ken), which makes the ongoing nature of the action a bit more explicit. Both are natural; okurken is very common and idiomatic.

Why are broşürü and sloganı marked with the -ı/-ü ending?

That is the definite accusative, used for specific, definite direct objects.

broşür → broşürü (“the brochure” as a specific object)
slogan → sloganı (“the slogan” as a specific object) Without the accusative, they would be indefinite (“a brochure,” “a slogan”): broşür okurken, bir slogan fark ettim.

Could sloganı mean “his/her/its slogan”? How do I tell?

The form sloganı is ambiguous out of context: it can be

accusative “the slogan,” or
nominative with 3rd person possessive “his/her/its slogan” (as a subject or topic), e.g., Onun sloganı çok kısa. In your sentence, after a verb, sloganı is clearly the definite object (“the slogan”). If you wanted “I noticed his slogan,” you’d say: Onun sloganını fark ettim (possessive + accusative).