Does Yosemite have a problem reaching alternate subnets? I know my question is a bit vague.  Read on.  

I have a static route set in my Asus router to bridge from one subnet to another (downstream router).  My Mavericks machine can connect to devices (via a web browser pointing to a devices' IP address control panel; for instance, a Brother printer) on this other subnet just fine but all (and I've tested 4!) Yosemite machines cannot.  I have also found that a Windows 10 machine connects just fine.  These Macs are all connected to the main router via wifi, DHCP and all options in network settings appear to be identical.  It appears to me that something changed in Yosemite.  btw, ping results via Terminal are basically identical on Yosemite and Mavericks.  0% packet loss to one of the intended targets and 100% packet loss to an unused address in the downstream subnet.  The only differences are just some expected variations in the ping times.

I have also found that a Lion computer (10.7.5) can also connect to the other subnet just fine.  Do I have something screwed up or is there a problem with Yosemite?
No - I've not had any issues with 10.10 or 10.11 with multiple subnets, multiple IP address per host and multiple network interfaces on a single OS/Mac.

I'd think something else is up. Are you familiar with the bonjour utility:

dns-sd -B _http
dns-sd -B _ipp


You can take the instance name and then dig up the IP address and cross reference it with arp -a to figure out many printing network issues...

mac:~ me$ dns-sd -L "Living Room HP D110" _ipp local.
Lookup Living Room HP D110._ipp._tcp.local.
DATE: ---Sat 28 Nov 2015---
12:44:33.139  ...STARTING...
12:44:33.584  Living\032Room\032HP\032D110._ipp._tcp.local. can be reached at hp.local.:631 (interface 4)
 txtvers=1 qtotal=1 pdl=application/vnd.hp-PCL,image/urf,image/jpeg rp=ipp/printer URF=CP1,MT1-2-8-9-10-11,OB9,OFU0,PQ3-4-5,RS300-600,SRGB24,W8,IS1 ty=Photosmart\ D110\ series product=\(HP\ Photosmart\ D110\ series\) usb_MFG=HP usb_MDL=Photosmart\ D110\ series priority=60 mac=68:b5:99:3e:a3:8b adminurl=http://hp.local. note=Family\ Room Color=T Duplex=F Scan=T
^C


Also, pings are the first packets to get dropped in most network overload scenarios, so try telnet on a known port (80 or 631 in this case) to get a reliable indication of health of the printer or device on the network.

You might need to handle IPv6 and IPv4 versions of the tools, too. (ping6 and telnet -6)