I'm not sure what will happen in this kind of scenario I'll share the photo of two diodes and basic connections below.
These two diodes tab points are actually connecting same node because of tab is connected to cathode of diode. Having something like this confugiration I will connect the diodes not only with PCB, with a heatsink too :),
So I am curious what you think about it.
Given the tabs are electrically connected, there is no short circuit here, so electrically there should be limited impact. Current may flow through the heatsink between the two cathodes as well as on the PCB, which may or may not be an issue.
You have to be careful through when it comes to what else the heatsink may attach to or touch - remember that it is floating at whatever voltage the cathode sits at. If that potential is not the same as say GND or the chassis, if it ever touched the chassis or some other ground point, there would be a short circuit. This can come as a suprise to anyone servicing the device. If this were a high voltage supply, it could present a major shock hazard if not insulated from the user/technitian.
To avoid any potential issues (pun intended), it is usually advisable to electically insulate the heatsink from the TO-220 tabs. You may also want to electrically connect the heatsink to the chassis/GND to avoid it floating with the capacitive coupling of the insulation.
If the thermal pads you have used between the cathodes are electrically conductive (the pad type ones usually aren't), they could be replaced with a non-electrically-conductive thermal pad. This would prevent direct contact between the tab and the heatsink.
You also have to account though for the screws as these contact both the heatsink and the tabs (probably the source of the connection in your setup). This is fixed by either using plastic (nylon) screws, or a TO-220 screw insulator bushing - this is a little peice of plastic like a washer that sits between the screw head and the tab, though they also have a little collar that feeds into the hole in the tab to make sure there are no shorts between the screw threads and the tab:
Depends on whether or not having a live circuit voltage on the exposed heatsink metal is acceptable. Many large companies have in-house design rule standards, and many of those prohibit this.
The circuit board trace connection is mandatory, and should be sized to handle 100% of the peak current continuously, plus a margin. The heatsink connection is a safety issue, not an electrical one.
