You can receive ALL call events by specifying in the filter each call event you want to receive (eCallBeginEvent, eCallDeliveredEvent, eCallEstablishedEvent, etc.
I do not know of a way to filter agent events only for a specific skill AND then get only call events for that skill only.

In an agent mode connection you will get all call and agent state events for that particular agent. If you are wanting to screenpop only calls for a specific skillgroup (any ACD call to the agent is destined for one of the agent’s skill groups) you can certainly examine the skillgroup id or skillgroup number in the begin call event and only screenpop on a specific skill or skills.

Thanks all for your replies, they are much appreciated. I'm specifically working in Monitor mode, capturing a required subset of notifications. My application is written in C#.
I need to then be able to obtain the SkillGroupId for that call which I'm currently not able to do. For instance, I'm looking in the args of the eCallHeldEvent which I can dump out as follows:
{(CallType:2 EventCause:65535 HoldingDeviceID:55523 EnablementMask:0xBF01A6 UniqueObjectID:call.5000.57282317.901582491100 CallStatus:eCallConnectionConnect EventID:11 MessageID:eCallHeldEvent ICMEnterpriseUniqueID:icm.150433.2939 DeviceUniqueObjectID:device.5000.901582491100)}
Taking this UniqueObjectID I'm able to obtain the Call object:
"(NumCTIClients:0 ConnectionCallID:0 CallType:10 ConnectionDeviceIDType:0 EventCause:65535 LineType:0 CampaignID:0 QueryRuleID:0 ANInull) UserToUserInfonull) DNISnull) DialedNumbernull) CallerEnteredDigitsnull) ConnectionDeviceIDnull) HoldingDeviceID:55907 RetrievingDeviceID:55907 CallWrapupDatanull) RouterCallKeyDay:0 RouterCallKeyCallID:0 EnablementMask:0x68BF000A UniqueObjectID:call.5000.57284972.55907 CallStatus:eCallConnectionHold MessageID:eCallHeldEvent ClassIdentifier:3 LastErrordotNET_Sess(32977404)_EvtThd(12):1) CallVariables) ICMEnterpriseUniqueID:icm.150433.3174 MeasuredCallQTime:0 DeviceUniqueObjectID:device.5000.55907)"
In the documentation the Call object has a properties for both SkillGroupID and SkillGroupNumber, which is what I'm looking for but are not there. I've read in various places in the documentation that it is possible to enable further properties through a registry setting on the CTI OS server, could that solve my problem?

I've got a question maybe a bit off the main topic: if you set the mentioned key to 0, what impact it has on the bandwidth used for client-server communication? Does Cisco bandwidth calculator for CTIOS take this option into account or do we need to calculate any overhead?