Your exact risks vary.
As another security-related story, unrelated to Wi-Fi (but I'll tie this all in momentarily), when Comcast started providing cable-based Internet in the late mid 1990s, there were reports of people signing up for the service at home, and then having Windows detect printers from other people's houses. So if they went to Microsoft Word and printed out a document, they may need to be careful about which printer they print to, or else a nice neighbor might call them up and say, "If you're looking for that document, I know right where it is!" (Similarly, people with printers could get strange documents being printed.)
Now, I haven't heard of such reports lately, so I'm assuming that got very fixed a long time ago. There are two potential ways for that to be fixed. One is changes made by Comcast (most likely). The other possible way would be changes by Microsoft. I believe these reports came in before 1998, and affected Windows 95 users. Changes in Windows 98, ME XP, Vista, 7, 8, 8.10, and 10 make it far less likely that such changes affect people today.
Now, with that background story, to answer your question: your exact risks will likely vary based on details of your network. If you run a home-based network where every device uses Windows 7, and never added security to anything, and opened up file sharing without a password required, but you have Windows Firewall turned on to provide the maximum protection that it can, then you're likely to have different risks than if you run a network where every computer is running a version of Windows Server 2003, with services hardened so that file sharing is completely disabled, but the Windows Firewall is disabled. And if you actually have a mixture of different types of computers, you're likely to have a different range of risks.
Operating systems and other types of software programs are computer code, and differences in that code (such as different operating systems, or different versions of the operating systems) can be one way that risks can be different. Other details can be things like whether you are running certain types of services, such as a network-based SQL (database) server. Other details are what kinds of sensitive information you have, and how that information is stored. (For example, as a college instructor, I didn't tend to have other people's credit card number or social security numbers on my computer, but I did have the first names of some students on a computer I used. Information about my taxes were stored on another computer, using password-protected file transfer methods that I used with less frequency.
Without knowing more details about your entire network, a full list of vulnerabilities/risks cannot be provided. In a nutshell, the risks are that a person can appear to be on a local network that is under your control. That can lead to other potential vulnerabilities, some of which are described by some of the other answers in this thread. A lot of network defenses are designed to protect against people who are not on the local network, and those defenses may be less effective, while other defenses may be unaffected. As a summary, I can say that quite a few of the precise risks will depend on details that typically vary between different individual computer networks.