A Happy Accident
Sydelle Pulaski is a mistake. Well, that's not all she is, but that's supposedly her biggest role in this mystery; her part was supposed to be played by someone else.
The private investigator Barney Northrup hired to investigate Sunset Towers' potential tenants confused Sybil Pulaski—the person they really wanted—with Sydelle Pulaski. While that might have been disastrous, it turned out to be fortuitous. Here's why:
First, Sydelle is a "character" in the crazy eccentric sense of the word. She's an overweight, overlooked secretary with a penchant for the dramatic, and she's really, really craving some attention. This means she goes so far as to totally make up an incurable illness, which she calls a "wasting disease," and to hobble around on crutches that she paints to match her clothing:
What good luck, the hobbling Sydelle Pulaski thought. Now she would really be noticed with such a pretty young thing for a partner. They might even invite her to the wedding. She'd paint a crutch white with little pink nosegays. (7.23)
What that translates to is annoyance for the other characters, and fun for us readers.
Second, without Sydelle, the real Mrs. Westing would have been found out much sooner. Since Sybil Pulaski was her childhood friend, it's fairly likely that she and the ex-Mrs. Westing would have recognized each other, perhaps even before the first will reading. That would have put a much different spin on the clues coming out, especially when they seem to be leading up to Mrs. Westing's alias.
Third, and perhaps most importantly, because of her secretarial training, Sydelle has the ability and the presence of mind to take notes on the will the first time it's read through. Okay, so the notes are in Polish shorthand and in that form they're useless to the rest of the characters, but as an idea they come in extremely handy during the trial scene, when the heirs have to look back over the will to figure out how else everything could have gone down. Without her copy of the will, the eventual winner might not have been able to solve the mystery.