Switch – If you turn on spanning tree, how do you know there is an issue with your network

That's correct. You should turn on spanning tree for any port that may potentially have another bridge(switch) plugged into it. The only negative effect this will have is a reconvergence of spanning tree any time you plug a new device into a VLAN. This means that when you plug in a new device the port will be placed into a blocking state and you won't be able to use that port until spanning tree figures out that it's safe to use. This usually takes anywhere from 10 seconds (rapid stp) to a minute (per vlan stp). If you have any ports that you absolutely need to come up immediately or that you know will never have another bridge plugged into them you can disable spanning tree on those ports. Also with spanning tree if you're using multiple vendors on your switches be sure to use a version of spanning tree that is compatible throughout your network.

The Spanning Tree Algorithm in use by 802.1d (STP), 802.1w (RSTP), and 802.1s (MST) states that the bridge (switch) with the lowest bridge ID (BID) will become the root bridge. The bridge ID is composed of a 2 byte priority value followed by a 6 byte MAC address (usually a burned in address [BIA] on the switch). As such, even if you were to configure two bridges with the same priority value -- their BID's would be different. The lower BID would win and become the root bridge.

Note that a feature known as "System ID" or MAC Address Reduction is often used changing the way the 2 byte priority value is used. In such a case, the 2 byte priority field is further broken into a 4 bit priority field and 12 bit VLAN ID field. This is used with Per-VLAN spanning tree, Rapid Per-VLAN Spanning Tree, and MST to hold both the priority of the bridge and the respective VLAN ID or MST instance number in the BPDU. Regardless of System ID, the overall lowest BID will always win/be root.

Recommend

1. Use Multi-Spanning Tree Protocol (MST/MSTP) instead of RSTP if you have a green field network and your devices support it. It scales better and requires less CPU as the number of VLANs increase.
2. Configure your aggregation switches (looks like a collapsed core) (RSW) with the lowest STP bridge priorities. Choose one as the lowest and root.
3. Leave your access/edge switches (ESW) alone as far as STP bridge priority is concerned. If both your aggregation switches fail (leaving you without an administratively configured STP root) the lack of administratively configured STP root will be the least of your problems.
4. Configure the relevant ports on the access/edge switches (ESW) with the fast link (Cisco calls it PortFast) feature.

Optional - The points below lock down spanning tree. Configure with caution.

1. If you desire, configure Root Guard (Cisco also calls the feature Root Guard) on the necessary access ports on the access/edge switches (except their uplinks to the core).
2. If you desire to lock down spanning tree even more than Root Guard, configure BPDU Guard (Cisco also calls the feature BPDU Guard) on the necessary access ports on the access/edge switches (except their uplinks to the core).

Note that Root Guard and BPDU Guard cannot be enabled at the same time. BPDU Filter is another option to explore but I recommend staying away from it as BPDU Filter can allow loops to form.