We finally got a Yosemite test machine giving me the chance to test yEd on Mac OSX 10.10.
For me, installation worked without problems. And I tested installing yEd from the yEd-3.13.dmg disk image with
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no Java installation at all
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only Java 7 in /Library/Java/JavaVirtualMachines/ (the default location for Oracle Java)
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only Java 7 in /System/Library/Java/JavaVirtualMachines/ (the OSX default location for Java)
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only Java 8 in /System/Library/Java/JavaVirtualMachines/
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both Java 7 and Java 8 in /Library/Java/JavaVirtualMachines/
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Java 6 in /System/Library/Java/JavaVirtualMachines/ and Java 7 and 8 in /Library/Java/JavaVirtualMachines/
Not once did I get "To open yed.app you need to install the legacy Java SE 6 runtime." According to Java SE 6 on Yosemite? this is not a yEd problem but general Yosemite/Java issue. Moreover, Eclipse Kepler for OS X Mavericks request Java SE 6 suggests that it is not even specific to Yosemite either. The top answer in the Stack Overflow thread also mentions a possible fix/workaround, by the way.
Regarding yEd slowing down the whole system, that was not the case for me either. However, I did test with a conventional 19" display using a 1280x1024 screen resolution. So, I cannot tell how yEd performs on high-resolution retina displays.