The qiblah of the mosque is different from that indicated by the compass
Question

                I'm a korean muslim who lives in korea. i bought one Qibla compass several months ago,and wanted to check it when i got it. I checked it in our masjid in Seoul, and it didn't indicate proper Qibla direction. I thought this compass was wrong, and told some muslim friends about it as a joke. And they said that they knew that our masjid is located not in the proper direction. after it, i got confused. For example when i do salat in the masjid with others, i stand as they do. but when i do salat by myself, i dont know what i have to do. Do i have to do salat as the compass shows? or as the masjid is located???
Praise be to Allah.Firstly, we are happy to learn that we have a 
    Muslim brother from Korea who is keen to understand his religion properly and to do acts of worship according to the conditions stipulated in 
    sharee’ah. We ask Allaah to make you steadfast in adhering to His religion and to make you more keen to understand Islam properly. 
With regard to the answer to your question, 
    it varies according to how great the deviation from the qiblah is – assuming that the compass is accurate. If the deviation is great – such as if 
    the qiblah is towards the west, and they are facing south, for example, then this deviation invalidates the prayer and the qiblah of the mosque 
    must be changed to the right direction. 
But if the deviation is slight, and is in the 
    same direction as the qiblah – such as if the qiblah is towards the west, and they deviate slightly towards the north-west or south-west, then 
    this does not matter and you should face this direction with them, because the ruling is that whoever is far away from the Ka’bah should face its 
    general direction and does not have to face it precisely. 
Al-Tirmidhi (344) narrated from Abu Hurayrah 
    that the Prophet  (peace and blessings of Allaah be upon him) said: “What is between the east and the west is qiblah.” (Al-Tirmidhi) said it 
    is hasan saheeh, and it was classed as hasan by al-Albaani in his commentary on Mishkaat al-Masaabeeh (715). See also question no.
    7535. 
You can define the correct direction of the qiblah quite easily by looking at a map and drawing 
    a straight line from your city to Makkah, and defining the direction of the qiblah on that basis. 
And Allaah knows best.