What to look out for when increasing network size

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http://serverfault.com – I'm a programmer by profession and don't understand this stuff all that well, so I apologise if this question is unclear, and I will try to keep improving it. I have a /24 IPv4 network, so approximately 255 IP addresses. Very soon we will have more than 250 devices on the network, and this number will continue to grow over time, therefore I have to expand the network capacity somehow. I am already making heavy use of DHCP to reduce the number of devices using an address at once. I can increase the size of the subnet to a /22, giving ~1024 IP addresses. If I do this, will there be issues with ()