The typical pros:
Concrete pads that widen.
Signage at each hole. (Although some distances don't match the on line scorecard)
Good use of elevation and the wooden areas in the park.
Mostly wooded with even the "open" holes having plenty of trees as obstacles.

The old grey baskets were difficult to see. Time to upgrade to the Innova bright yellow style.

The flow of the course wasn't great. Some overlap as #6 uses a weak mando to the left to avoid throwing at basket #1. Some excess walking- 4 to 5, 7 to 8 come to mind.

Looks like the older course that it is. Wasn't an awful course, just need to redo a couple of holes to give it a wow hole or two.
Have played there three times. Won't rush to come back, but if friends wanted to play, would be willing to go.

Just an addendum, really, to the other reviews, which seem to sum up my thoughts on this course. I recommend playing Bluebird, Schroeder and Watson trails all in one day. They are close to one another (about 10-15 minutes), they are all 9 holes, and all have their strong points. The more they are played, the more attention they will receive.

Schroeder Park is a pretty basic course. There are two uphill shots, three elevated tees, three heavily wooded shots and enough trees on the rest of the shots that you can easily hit one. All of the shots are in 180 ft-300ft range, so every hole is deuceable. It is not a championship course or a place where you can really air it out, but you can have a good time here.

The tees are bad. A lot of them are not level, and the tee sign for # 4 is in the middle of the tee. They have spread woodchips to keep them from washing out, but they are not good. There used to be multiple tees, but currently I can only find one set of marked tees.[UPDATE: The course now has one concrete tee per hole; you can ignore all my bitching about the old dirt tees.]
There has been a long-standing dispute with the homeowners across the street for holes # 5 & # 6. They campaign to have the course removed on a regular basis. This spring both of those holes were moved up the hill to move them away from those homes, and as a result the tee for # 5 is dangerously close to the basket for # 2 and the fairway for # 6 runs needlessly close to the pin for # 1. [UPDATE: Hole 6 now has a mando to keep you from throwing over #1's basket.]
The fairways for holes #7 & #8 are not being cleared of underbrush, so you can throw a pretty good shot and have a hard time finding your disc.
The course itself is hidden behind a big aquatic park and hard to find if you don't know where to look. Once you play # 1, you can see holes in both directions with nothing to indicate which way to go, so a new visitor may end up wandering around. You could easily get lost going from hole 3 to hole 4, hole 4 to hole 5, and hole 7 to hole 8. Directional signs would make this an easier place for players new to the park to find their way around.

This course was the first original course design by Dave McCormack of Gateway Disc Sports. The course was actually designed and installed for free to help build the GDS course design resume. For a short time the relationship with the City of Manchester and the local disc golf community was very good, and an expanded 18 hole layout was used here in for the 1997 & 1998 Gateway Open. That layout featured many heavily wooded holes and was a tournament-quality course. There was talk of that layout becoming a permanent 18 hole course, but problems with the behavior of some disc golfers quickly dashed those hopes. Nothing has been done to improve this course since it was installed, but it has survived repeated attacks by the neighbors to have the course removed.
As is stands there is no reason to go out of your way to visit this course. However if you are in West St. Louis County you can combine this course with the 9 holes at Bluebird Park (about 10 minutes to the West) and have an enjoyable day of disc golf. It may not be a championship-type course, but if every town in the US had a course like Schroeder Park disc golf would be in good shape.