You have what two what are called flat networks, one for the 10.100.0.0/16 Subnet and one for 10.101.0.0/16 subnet.
Broadcast and arp would indeed be an issue in this network and your experience seems to confirm this. every arp is broadcast throughout the flat network.
You can happily subnet your network using class C subnet masks but you will need a layer 3 device to ensure that the IP traffic can route between subnets.
So if I may be so bold here is a tried and tested formula for doing this.
1) Work out how many VLANs you need, this is done on whichever criteria you wish, geographic (ie, all PCs in the same area of the office and maybe off the same switch have their own VLAN) or along business lines (Seperating Finance from Sales from HR) It is entirely up to you, but do it before you start.
2)Make the base subnet 10.100.1.0/24 your management VLAN thus the IP addresses of all switches sit in here and any network management server or workstation make this VLAN 1
3)Make one subnet contain all your servers and internet gateway say 10.100.2.0/24. Make the gateway address either 10.100.2.1. or 10.100.2.254. The other VLANs are allocated as you see fit.
4) On the layer 3 device make sure each subnet has a routable IP address to be used as the default gateway for each client and server. Ultimately your networks default gateway is going to be the exit point of your network either your firewall or WAN port etc.
5) Make sure the layer 3 device routes between subnets and ensure it does not broadcast the routing tables to any other subnets than that with your network default gateway device on. Try not to use RIP version 1 if possible, RIP v2 is ok.
6) configure your clients, the time consuming bit you will have to change every PC and printer and any other such device on the network to have an IP address in the correct subnet and with the correct default gateway. Depending on the number of devices involved this could be a long and arduous manual process, but the subnet mask at least in every case must change. DHCP may help here, the layer 3 device should be able to forward DHCP requests from clients to the DHCP server.
7) Active directory will complicate matters in ways too complex to go through here.
8) IPX/SPX will really complicate matters, if you have servers and applications using IPX/SPX you may have fun finding a layer 3 switch that will successfully route or broadcast the IPX traffic between VLANs, support for IPX/SPX is becoming less and less common. If this is a major issue it could easily explain the flat network architecture.
The success of this will in almost all ways depend on the planning you undertake before you start.